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Getting in front of pharma: Automated public discovery of drug candidates

11.30.2018 | projects

A couple weeks ago Sean and I were fortunate enough to participate in another edition of Rhizome's 7x7, this time in Beijing in collaboration with the Chinese Central Academy of Fine Arts (CAFA). I was very excited to collaborate with Sean again after our first collaboration in New York at the New Museum, and to have the chance to try something different together.

We thought about revisiting our previous project, cell.farm, which was a proposal for a cryptocurrency/distributed computing system for which the proof-of-work protocol involved computing simulation updates for an atomic-level model of a human cell (though our proposal initially suggested simulating a ribosome). Such detailed simulation of biological processes would be a boon for medical research, but simulating even the simplest cell at that resolution is so computationally demanding that it's infeasible even for the world's best supercomputers. But the aggregate computing power of the Bitcoin network is orders of magnitudes larger than any supercomputer, and might be able to run such a model in a reasonable amount of time. By adopting that model for in silico cells, a crucial part of medical research is essentially collectivized, and as part of our design, so too are the results of that research. The project bears similarity to Folding@Home and its crypto-based derivatives (e.g. FoldingCoin), but as far as I know none of these projects explicitly distribute ownership of the research that results from the network. There were also some design details that we didn't have time to hash out, and we left open a big question of computational verifiability: given a simulation update from a node, how can you be certain that they actually computed that value rather than returned some random value? (Golem has this problem too, the difficulty of which is discussed a bit here).

This time around, rather than a project about medical research abstractly, we focused specifically on the pharmaceutical industry, the 1.1 trillion dollar business lying at the nexus of intellectual property law, predatory business practices, and the devaluing of human life.

The pharmaceutical industry

(For background I'm going to lean heavily on the "Pill of Sale" episode of the Ashes Ashes podcast which goes into more detail about the pharmaceutical industry -- definitely worth a listen.)

Most Americans are familiar with exorbitantly-priced drugs -- if not directly than via one of the many horrifying stories of people crowdfunding their continued existence or flying elsewhere to access more reasonable prices. A hepatitis C cure from Gilead, Solvadi, costs $84,000 for a 12-week course and is the subject of a recent Goldman Sachs report. The report describes cures as effective as Solvadi (up to 97%) as bad for business since you cure yourself out of a market. Even something as common insulin can cost a significant portion of income -- to the point where people die from needing to ration it. This hostile environment is thinly justified with rhetoric around drug development costs and enforced through the patent law system, all under the implicit, sometimes explicit, assumption that it is necessary for drug companies to make a profit on their drugs. Patents provide exclusive rights for a company to sell a particular drug; this temporary monopoly essentially gives them carte blanche to set whatever price they want so that they recoup the drug development costs, so the story goes. These patents last 20 years and can basically be extended by "exclusivity" periods which add up to another 7 years. A drug may take 10-15 years to develop, leaving a window of at least 5 years of exclusive rights to produce and sell it. "Orphan drugs", drugs that treat rare conditions, may have longer monopolies to compensate for the smaller market size. After this period generics are permitted to enter the market, which drives the cost down, but there are all sorts of tricks available that can prolong this protection period even further, a practice called "evergreening". For example, slightly modifying how the drug is delivered (e.g. by tablet or capsule) can be enough for it to essentially be re-patented. (It's worth noting that prices can be high even for generics. For example, epinephrine -- commonly known as an EpiPen, essential for severe allergic reactions -- can be bought for about 0.10-0.95USD outside the US, whereas generics in the US can cost about$70.)

Drug development is expensive, averaging at over $2.5 billion per drug, and that's only counting for those that gain FDA approval. However, these exclusivity rights are not merely used to recapture R&D costs, as is often said, but instead to flagrantly gouge prices such that the pharmaceutical industry is tied with banking for the largest profit margins of any industry (as high as 43% in the case of Pfizer). The narrative around high drug development costs also takes for granted that pharmaceutical companies are the ones bearing all of these costs. A considerable amount of the basic research that is foundational to drug development is funded publicly; the linked study found that public funding contributed to every drug that received FDA approval from 2010-2016. The amount of funding is estimated to be over$100 billion.

It used to be that inventions resulting from federal funding remained under federal ownership, but the 1980 Bayh–Dole Act offered businesses and other institutions the option to claim private ownership. The result is the public "paying twice" for these drugs. The Act does preserve "march-in rights" for the government, allowing the government to circumvent the patent and assign licenses independently if the invention is not made "available to the public on reasonable terms", but as of now these rights have never been exercised. In 2016 there was an unsuccessful attempt to use these march-in rights to lower the price of a prostate cancer drug called Xtandi, priced at \$129,000/year.

All of this isn't to say that the work of the pharmaceutical industry isn't valuable; drugs are a necessary part of so many peoples' lives. I recently started using sumatriptan to deal with debilitating migraines, and am hugely grateful it exists (and is not ridiculously expensive). It's because pharmaceuticals are such a critical part to life that their development and distribution should not be dictated the values that currently shape it.

One particularly egregious example of this mess is the nightmare scenario of Purdue Pharmaceuticals, owned by the Sackler family (who are also prolific patrons of the arts), producers of OxyContin (accounting for over 80% of their sales last year), basically responsible for the ongoing opioid crisis (affecting at least 2.1 million Americans directly, and many more collaterally), and recently granted a patent for a drug that treats opioid addiction. The patented treatment is a small modification of an existing generic.

The day before our 7x7 presentation a story broke in the Guardian: "Sackler family members face mass litigation and criminal investigations over opioids crisis".

Computational drug discovery

One reason drug development is so difficult is that the space of possible drug compounds is extremely large, estimated to be between 1060 and 1063 compounds. For comparison, there are an estimated 1022 to 1024 stars in the entire universe, and according to this estimate about 1049-1050 atoms making up our entire world.

Drug development is in large part a search problem, looking to find useful compounds within this massive space. A brute-force search is impossible; even if it took only a couple seconds to examine each possible compound you'd see several deaths of our sun (a lifespan of about 10 billion years) before fully exploring that space.

More effective techniques for searching this space include slightly modifying existing drugs for different therapeutic applications ("me-too" compounds) and literally looking at plants and indigenous medical traditions for leads (this general practice is called "bioprospecting" and this particularly colonialist form is called "biopiracy").

Of course with the proliferation of machine learning there is a big interest in searching this space computationally. Two main categories are virtual screening (looking through known compounds for ones that look promising) and molecular generation (generating completely new compounds that look promising). We focused on molecular generation for reasons described below.

A primary goal for matter.farm is to publicize this work in computational drug discovery and also help researchers use these generated compounds as potential leads for new beneficial drugs. With our system, which is also open source, independent and institutional researchers alike can access automated drug discovery technology and hopefully accelerate the drug development process.

Prior art and public discovery of drugs

(For this section we spoke with a patent lawyer who requested that we note that they are not representing us.)

One crucial criteria for a patent is that the invention must be novel; that is, the invention cannot have already been known to the public. An existing publicly-known instance of an invention is called "prior art" and can invalidate a patent claim. However, sufficient variations to an invention may qualify it as original enough to be patentable (this is the idea behind evergreening, described above).

If a drug is discovered and made public prior to a patent claim on it, it would function as prior art and make that compound un-patentable in its current form. If we were able to generate new molecules that could function as useful drugs, and make public those new molecules, then perhaps we can prevent companies from patenting them and maintaining a temporary monopoly on their distribution.

This is the second goal of matter.farm: develop an automated drug discovery system to find and publish useful drugs so they cannot be patented.

Other efforts to the address problems with pharmaceutical industry can be found in initiatives like Medicare for All and the proposed Prescription Drug Price Relief Act, and the organizing happening around those. The issues with the pharmaceutical industry are just one piece of a more general hostility in American healthcare.

There is also a burgeoning DIY medicine movement which aim to build alternatives to industrialized medicine, providing autonomy, access, and reliability where those are normally withheld. For example, the artist Ryan Hammond is working on genetically modifying tobacco plants to produce estrogen and testosterone, and the Four Thieves Vinegar Collective (discussed in the Ashes Ashes "Pill of Sale" episode) provides instructions for a DIY EpiPen and a DIY lab ("MicroLab") for synthesizing various pharmaceuticals, including Naloxone and Solvadi.

That's it for the background of the project. The following section describes how the system works in more detail.

How it works

The complete matter.farm system involves three components:

1. A molecular generation model, using a version of the graph variational autoencoder ("JTNN-VAE") described in [2], modified to be conditional ("JTNN-CVAE"). This generates new compounds given a receptor and action, e.g. a nociceptin receptor agonist.
2. An ATC code prediction model. The Anatomical Therapeutic Chemical (ATC) classification system categorizes compounds based on their therapeutic effects. We use this to estimate what a generated compound might treat.
3. A retrosynthesis planner. Retrosynthesic analysis is the process of coming up with a plan to synthesis some target compound from an inventory of base compounds (e.g. compounds you can purchase directly from a supplier). This is necessary to meet the enablement requirement of prior art; that is, it's not enough to come up with a new compound, you also need to sufficiently demonstrate how it could be synthesized.

To train these various models we relied on a number of public data sources, including PubChem, UniProtKB, STITCH, BindingDB, ChEMBL, and DrugBank.

Chemical compounds can be represented in a number of ways, e.g. as a 2D structural diagram or a 3D model. One of the most portable formats is SMILES, which represents a molecule as an ASCII string, and is what we use throughout the project.

Clustering

For training the JTNN-CVAE model we needed to cluster the compounds in a meaningful way. At first we didn't look at receptors and actions but rather tried to leverage the vast published chemical research literature (in PubMed) and USPTO patents.

For the first attempt we tried learning word2vec embeddings from PubMed article titles and abstracts, then representing documents using TF-IDF as described in the WISDM algorithm, and finally clustering using DBSCAN or OPTICS. This ended up being way too slow, memory intensive, and limited in what clustering algorithms we could try.

The second attempt involved generating a compound graph such that an edge exists between compound A and B if they appear in an article or patent together. So instead of linking compounds based on the content of the articles they're mentioned in, they're linked solely on the virtue of being mentioned together in an article, under the assumption that this indicates some meaningful similarity. Then we ran a label propagation community detection algorithm to identify clusters within the graph. The graph was fairly sparse however and in the end looking at the connected components seemed to be enough. There were still some limitations with speed and memory that led us to abandon that approach.

Finally we decided to cluster based on receptors compounds were known to interact with. This reduced the amount of compounds we were able to look at (since the compounds for which receptor interactions are known are much less than the total of all known compounds), but the data was richer and more explicit than co-mentions in text documents. A drug's effects are determined by the receptor it targets and how it interacts with that receptor (does it activate it, does it block it, etc). For instance, OxyContin is a mu-type and kappa-type opioid receptor agonist (it activates them), and Naloxone (used to treat opioid overdose) is a mu-type and kappa-type opioid receptor antagonist (it blocks them).

The ChEMBL data has information about both receptors and the type of interaction (agonist, antagonist, etc), whereas BindingDB has information about only the receptors but for more compounds. So we used a two-pass approach: for the first pass, we create initial clusters based on receptor-action types and on the second-pass we augment these clusters with the BindingDB compounds, assigning them to the cluster that matches their target receptor and has the highest fingerprint similarity to the cluster's current members. This resulted in 461 receptor-action clusters.

Molecular generation model

The JTNN-VAE model described in [2] is a variational autoencoder that handles molecular graphs. A variational autoencoder is a generative model that learns how to compress ("encode") data in such a way that it can be reliable decompressed ("decoded"). It accomplishes this by learning an underlying probability distribution that describes the data. Once the model has learned this distribution you can sample it to generate new data that looks like the old data. This post provides an overview on variational autoencoders.

We modified the model to be conditional, allowing us to sample from the learned probability distribution conditioned on the cluster (the receptor-action) we want to generate new compounds for.

ATC code prediction model

The ATC code prediction model is a straightforward multiclass neural network. Though ATC code prediction is technically a multilabel problem (a compound may have more than one ATC code), most compounds had only one code, so we treated it as a multiclass problem. ATC codes have 5 levels, from low detail to high detail; we predict level 3 codes ("pharmacological/therapeutic/chemical subgroup"), with one class for each level 3 code. We use 2048-bit Morgan fingerprints as representations for the compounds and achieved about 80% accuracy with this naive approach -- not ideal, but fine for our purposes and time constraints.

Retrosynthesis planner

Here's where it came down to the wire. We attempted to implement the model ("3N-MCTS") described in [7], which involves Monte Carlo Tree Search (MCTS) and three policy networks. The policy networks predict what reaction rules might apply to a given compound. The paper's model is trained on Reaxys data, which is way too expensive for us, so we used a smaller dataset extracted from USPTO patents (from [26]). Our implementation is basically complete but we didn't have enough time to train the models.

In an 11th-hour Hail Mary we used MIT's ASKCOS system which got us mostly partial synthesis plans. At some point we should revisit the 3N-MCTS system to see if we can get that working.

Sampling and filtering

Once all the models were ready we sampled 100 new compounds for each of the 461 receptor-action clusters. Then we filtered down to valid compounds (with no charge) and to those not present in PubChem's collection of 96 million compounds. We ended up whittling the set down to about 15,000 new compounds for which we then predicted ATC codes and generated synthesis plans.

Future work

Time was fairly tight for the project so we didn't get to tune or train the system as much as we wanted to. And it would have been nice to try to experiment with more substantial modifications of the models we used. But for me this project was a wonderful learning experience and renewed an interest in chemistry. I want to spend some more time in this area, especially in materials science because of its relevance to lower-impact technologies, such as this cooling material.

References

1. Botev, Viktor, Kaloyan Marinov, and Florian Schäfer. "Word importance-based similarity of documents metric (WISDM): Fast and scalable document similarity metric for analysis of scientific documents." Proceedings of the 6th International Workshop on Mining Scientific Publications. ACM, 2017
2. Jin, Wengong, Regina Barzilay, and Tommi Jaakkola. "Junction Tree Variational Autoencoder for Molecular Graph Generation." arXiv preprint arXiv:1802.04364 (2018).
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11. Community Detection in Python
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20. Kim S, Thiessen PA, Bolton EE, Chen J, Fu G, Gindulyte A, Han L, He J, He S, Shoemaker BA, Wang J, Yu B, Zhang J, Bryant SH. PubChem Substance and Compound databases. Nucleic Acids Res. 2016 Jan 4; 44(D1):D1202-13. Epub 2015 Sep 22 [PubMed PMID: 26400175] doi: 10.1093/nar/gkv951.
21. Gilson, Michael K., et al. "BindingDB in 2015: a public database for medicinal chemistry, computational chemistry and systems pharmacology." Nucleic acids research 44.D1 (2015): D1045-D1053.
22. The UniProt Consortium. UniProt: the universal protein knowledgebase. Nucleic Acids Res. 45: D158-D169 (2017)
23. Gaulton A, Hersey A, Nowotka M, Bento AP, Chambers J, Mendez D, Mutowo P, Atkinson F, Bellis LJ, Cibrián-Uhalte E,
Davies M, Dedman N, Karlsson A, Magariños MP, Overington JP, Papadatos G, Smit I, Leach AR. (2017)
'The ChEMBL database in 2017.' Nucleic Acids Res., 45(D1) D945-D954.
24. Papadatos, George, et al. "SureChEMBL: a large-scale, chemically annotated patent document database." Nucleic acids research 44.D1 (2015): D1220-D1228.
25. Lowe, Daniel Mark. Extraction of chemical structures and reactions from the literature. Diss. University of Cambridge, 2012.
26. Lowe, Daniel (2017): Chemical reactions from US patents (1976-Sep2016). figshare. Fileset. CC0 License.
27. Liu, Bowen, et al. "Retrosynthetic reaction prediction using neural sequence-to-sequence models." ACS central science 3.10 (2017): 1103-1113.
28. Klucznik, Tomasz, et al. "Efficient syntheses of diverse, medicinally relevant targets planned by computer and executed in the laboratory." Chem 4.3 (2018): 522-532.
29. Segler, Marwin HS, and Mark P. Waller. "Neural‐Symbolic Machine Learning for Retrosynthesis and Reaction Prediction." Chemistry–A European Journal 23.25 (2017): 5966-5971.
30. Law, James, et al. "Route designer: a retrosynthetic analysis tool utilizing automated retrosynthetic rule generation." Journal of chemical information and modeling 49.3 (2009): 593-602.
31. Schwaller, Philippe, et al. "“Found in Translation”: predicting outcomes of complex organic chemistry reactions using neural sequence-to-sequence models." Chemical science 9.28 (2018): 6091-6098.
32. Kipf, Thomas N., and Max Welling. "Semi-supervised classification with graph convolutional networks." arXiv preprint arXiv:1609.02907 (2016).
33. Yang, Zhilin, William W. Cohen, and Ruslan Salakhutdinov. "Revisiting semi-supervised learning with graph embeddings." arXiv preprint arXiv:1603.08861 (2016).
34. Kipf, Thomas, et al. "Neural relational inference for interacting systems." arXiv preprint arXiv:1802.04687 (2018).
35. Wei, Jennifer N., David Duvenaud, and Alán Aspuru-Guzik. "Neural networks for the prediction of organic chemistry reactions." ACS central science 2.10 (2016): 725-732.
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37. Gupta, Anvita. "Predicting Chemical Reaction Type and Reaction Products with Recurrent Neural Networks."
38. Plehiers, Pieter P., et al. "Automated reaction database and reaction network analysis: extraction of reaction templates using cheminformatics." Journal of cheminformatics 10.1 (2018): 11.
39. MIT's ASKCOS ("Automated System for Knowledge-based Continuous Organic Synthesis")

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# Difference between revisions of "2016 AMC 10B Problems/Problem 20"

## Problem

A dilation of the plane—that is, a size transformation with a positive scale factor—sends the circle of radius $2$ centered at $A(2,2)$ to the circle of radius $3$ centered at $A’(5,6)$. What distance does the origin $O(0,0)$, move under this transformation?

$\textbf{(A)}\ 0\qquad\textbf{(B)}\ 3\qquad\textbf{(C)}\ \sqrt{13}\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5$

## Solution 1: Algebraic

The center of dilation must lie on the line $A A'$, which can be expressed as $y = \dfrac{4x}{3} - \dfrac{2}{3}$. Note that the center of dilation must have an $x$-coordinate less than $2$; if the $x$-coordinate were otherwise, then the circle under the transformation would not have an increased $x$-coordinate in the coordinate plane. Also, the ratio of dilation must be equal to $\dfrac{3}{2}$, which is the ratio of the radii of the circles. Thus, we are looking for a point $(x,y)$ such that $\dfrac{3}{2} \left( 2 - x \right) = 5 - x$ (for the $x$-coordinates), and $\dfrac{3}{2} \left( 2 - y \right) = 6 - y$. We do not have to include absolute value symbols because we know that the center of dilation has a lower $x$-coordinate, and hence a lower $y$-coordinate, from our reasoning above. Solving the two equations, we get $x = -4$ and $y = - 6$. This means that any point $(a,b)$ on the plane will dilate to the point $\left( \dfrac{3}{2} (a + 4) - 4, \dfrac{3}{2} (b + 6) - 6 \right)$, which means that the point $(0,0)$ dilates to $\left( 6 - 4, 9 - 6 \right) = (2,3)$. Thus, the origin moves $\sqrt{2^2 + 3^2} = \boxed{\sqrt{13}}$ units.

## Solution 2: Geometric

$[asy] /* Geogebra to Asymptote conversion, documentation at artofproblemsolving.com/Wiki, go to User:Azjps/geogebra */ /* by adihaya */ import graph; size(13cm); real labelscalefactor = 0.5; /* changes label-to-point distance */ pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps); /* default pen style */ real xmin = -7., xmax = 9., ymin = -7., ymax = 9.6; /* image dimensions */ pen xdxdff = rgb(0.49019607843137253,50.49019607843137253,1.); pen uuuuuu = rgb(0.666666666,0.26666666666666666,0.26666666666666666); pen qqzzff = rgb(0.,0.6,1.); pen ffwwqq = rgb(1.,0.4,0.); pen qqwuqq = rgb(0.,0.39215686274509803,0.); pair O = (3.,0.), A = (2.,2.), B = (2.,1.), C = (4.203155585,5.592712848525), D = (5.,4.), F = (-3.999634206191805,-5.999512274922407), G = (-3.999634206191812,-5.9995122749224175); /* by adihaya */ draw((2.482656878,0.)---(4.482568783,0.48268779)--(2.,0.48272202065687797)--B--cycle, qqwuqq); draw((5.482722020656878,0.)--(7.4827220878,1.48277797)--(5.,0.48272687797)--(5.,0.)--cycle, qqwuqq); Label laxis; laxis.p = fontsize(10); xaxis(xmin, xmax, Ticks(laxis, Step = 2., Size = 2, NoZero),EndArrow(6), above = true); yaxis(ymin, ymax, Ticks(laxis, Step = 2., Size = 2, NoZero),EndArrow(6), above = true); /* draws axes; NoZero hides '0' label */ /* draw figures */ draw(shift(A) * scale(2., 2.)*unitcircle); draw(shift((5.,6.)) * scale(3.000060969351735, 3.000060969351735)*unitcircle); draw((xmin, 1.3333333333333333*xmin-0.6666666666666666)--(xmax, 1.3333333333333333*xmax-0.6666666666666666)); /* line */ draw((2.,ymin)--(2.,ymax)); /* line */ draw((5.,ymin)--(5.,ymax)); /* line */ draw((xmin, 1.6666869897839114*xmin + 0.6666260204321771)--(xmax, 1.6666869897839114*xmax + 0.6666260204321771)); /* line */ draw(O--F, qqzzff); draw(F--A, ffwwqq); /* dots and labels */ dot(O,blue); label("O", (0.08696973475182286,0.23426871275979863), NE * labelscalefactor,blue); dot(A,blue); label("A", (2.089474351594523,2.23677332960249), NE * labelscalefactor,blue); dot((5.,6.),blue); label("A'", (5.093231276858573,6.2190268290055695), NE * labelscalefactor,blue); dot(B,xdxdff); label("B", (2.089474351594523,0.23426871275979863), NE * labelscalefactor,xdxdff); label("c", (0.9971991060439592,3.2607813723061394), NE * labelscalefactor); dot(C,xdxdff); label("C", (3.2955282685566036,3.829674729363722), NE * labelscalefactor,xdxdff); label("d", (3.477574142815031,8.107752774436745), NE * labelscalefactor); label("a", (7.255026033677397,9.404829628528034), NE * labelscalefactor); label("b", (2.1804972887237364,9.404829628528034), NE * labelscalefactor); label("e", (4.615360856930201,9.404829628528034), NE * labelscalefactor); dot(D,linewidth(3.pt) + uuuuuu); /* Solution by adihaya */ label("D", (2.089474351594523,4.125499275033665), NE * labelscalefactor,uuuuuu); dot((5.,9.000060969351734),linewidth(3.pt) + uuuuuu); label("E", (5.093231276858573,9.131760817140394), NE * labelscalefactor,uuuuuu); label("f", (4.933941136882449,9.404829628528034), NE * labelscalefactor); dot(F,linewidth(3.pt) + uuuuuu); label("\Large{(-4,-6)}", (-3.73599362467515,-6.273871291978948), NE * labelscalefactor,uuuuuu); label("\Large{2\sqrt{13}}", (-2.916787190512227,-2.0868161840351394), NE * labelscalefactor,qqzzff); dot(G,linewidth(3.pt) + uuuuuu); label("G", (-3.9180394989335774,-5.864268074897489), NE * labelscalefactor,uuuuuu); label("\Large{10}", (0.2690156090102501,-0.6759606585323339), NE * labelscalefactor,ffwwqq); clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); /* re-scale y/x */ currentpicture = yscale(0.9090909090909091) * currentpicture; /* end of picture */[/asy]$ Using analytic geometry, we find that the center of dilation is at $(-4,-6)$ and the coefficient/factor is $1.5$. Then, we see that the origin is $2\sqrt{13}$ from the center, and will be $1.5 \times 2\sqrt{13} = 3\sqrt{13}$ from it afterwards.

Thus, it will move $3\sqrt{13} - 2\sqrt{13} = \boxed{\sqrt{13}}$.

## Solution 3: Logic and Geometry

Using the ratios of radii of the circles, $\frac{3}{2}$, we find that the scale factor is $1.5$. If the origin had not moved, this indicates that the center of the circle would be $(3,3)$, simply because of $(2 \cdot 1.5, 2 \cdot 1.5)$. Since the center has moved from $(3,3)$ to $(5,6)$, we apply the distance formula and get: $\sqrt{(6-3)^2 + (5-3)^2} = \boxed{\sqrt{13}}$.

## Solution 4: Simple and Practical

Start with the size transformation. Transforming the circle from $r=2$ to $r=3$ would mean the origin point now transforms into the point $(-1,-1)$. Now apply the position shift: $3$ to the right and $4$ up. This gets you the point $(2,3)$. Now simply apply the Pythagorean theorem with the points $(0,0)$ and $(2,3)$ to find the requested distance.

## Solution 5: Using the Axes

Before dilation, notice that the two axes are tangent to the circle with center $(2,2)$. Using this, we can draw new axes tangent to the radius 3 circle with center $(5,6)$, resulting in a "new origin" that is 3 units left and 3 units down from the center $(5,6)$, or $(2,3)$. Using the distance formula, the distance from $(0,0)$ and $(2,3)$ is $\boxed{\sqrt{13}}$. ~Mightyeagle


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# How do you solve the following system?: -2x+12y=-20 , y=1/3x

Aug 23, 2016

$x = - 10$

$y = - \frac{10}{3}$

#### Explanation:

$- 2 x + 12 y = - 20$

or

$2 x - 12 y = 20$

or

$x - 6 y = 10$

$y = \frac{x}{3}$

or

$x = 3 y$

Plugging the value $x = 3 y$ in the equation $x - 6 y = 10$

We get

$3 y - 6 y = 10$

or

$- 3 y = 10$

or

$y = - \frac{10}{3}$--------------------------Ans $1$

Plugging the value
$y = - \frac{10}{3}$ in the equation $x = 3 y$ we get

$x = 3 \times \left(- \frac{10}{3}\right)$

or

$x = - 10$-----------------------------Ans $2$


text:
# how to calculate yield of finished product

9:;<9= F = ࠵? For calculating yield of finished goods(actuals) , the formula is  = Actual voulme (Qty) of Production divided by actual volume (Qty) of Raw materials consumed, Percentage yield = Actual Yield divided by Standard yield, Posted 7 years ago by By creating an account you will be able to shop faster, be up to date on an order status, and keep track of the orders you have previously made. How Do You Estimate Actual Yield? Calculate it by dividing the number of "good" units you produce by the number of units entering the production process. At this point, we need to calculate or estimate the amount of raw material that will be required to manufacture one single product, including the scrap generated in the process. This video shows you how to calculate the theoretical and percent yield in chemistry. The coefficients of each product, if the reaction is balanced, tells you the amount to expect, in molecular ratios. That’s the customary way of doing it around here, but there’s a better way.”, “Unit yields often have very little to do with costs,” Peter continued. Yield testing is useful for standardizing the cost of finished products, monitoring the use of raw materials, forecasting quantities for orders, and standardizing recipes and portion sizes. The actual yield is the actual amount you created, measured directly on a scale. Yield testing is useful for standardizing the cost of finished products, monitoring the use of raw materials, forecasting quantities for orders, and standardizing recipes and portion sizes. The calculation of yield variance is: (Actual output in units - Expected output in units) x Standard cost … Actual yield is the amount of product you actually got while theoretical is the maximum possible yield. Common Product Yields VEGETABLES Acorn Squash Flesh Raw 74% Eggplant Trim, Pared, and Sliced 81% Artichoke Edible Leaves and Base 40% Endive Trimmed and Cored 86% Asparagus Trimmed Ends 80% Fennel Trimmed and Cored 86% Beets Peeled and … Yield = 6%. View I do not want to refer the production order. Guideline on manufacture of the finished dosage form EMA/362427/2017 Page 6/15 : strategies may be : Sam handed Peter a computer printout and asked, “If the yields are so high, why is my efficiency so low?”. Finished Goods Inventory, as the name suggests, contains any products, goods, or services that are fully ready to be delivered to customers in final form. The Food Cost Yield Calculator is a flexible Microsoft Excel® set of spreadsheets designed to aid restaurant owners, chefs, and managers in determining the true cost of the raw products used to produce menu items. Explanation of the Total Production Cost Formula. Peter, a Lean Six Sigma Black Belt, studied the report for a moment and then nodded. % yield = 100 x actual mass of product / theoretical mass of product = 100 x 162 / 204 = 79.4% (2 sf) (9) Rather than here, I've added more % yield calculations to the Reacting mass ratio calculations of reactants and products from equations page. Indeed, every finished product manufacturing process should have an associated control strategy suitable for its intended purpose . By including the rework process in the multiplication product, we would get an artificially low yield. The current yield is .0619 or 6.19%, here's how to calculate: ($57.50 coupon /$928.92 current price). This is what is known as the edible portion of your product. Calculate the theoretical yield of calcium carbonate, identify the limiting reactant, and given an actual yield of 6.35g, calculate the percent yield. Regards, Shailendra Please suggest that how we can calculate the percentage of item wise yield on finished products and also in case where mix RM has been used for producing the items. The percentage yield shows how much product is obtained compared to the maximum possible mass. What is his percent yield? The following chemical reaction was carried out in a hood in a university laboratory. In a lab, a scientist calculate he should produce 12.3 grams of product in his experiment. Calculating the Property/Capital Value: Capital Value = (£150,000 / 6) x 100. For Example to produce 80 tons of FG, we require 100 tons of Rm, then yield is calculated as  80/100 = 80%. The information about ‘yield’, ‘percentage of yield’, and ‘shortages/excess’ is required to be given only to the extent such information is available in the records of the business. 1 − ࠵? If we only look at unit yields, they look much different. Also, processes can break down, leading to production slowdowns and stoppages. © 2020 Pyzdek Institute, LLC. Covenant Strength & its Effect on Property Yield. = 0.5 1 − (0.3×0.8) = 0.66 Second, compute the average cost to process one unit of material in Rework part 1. Food Cost Yield Calculator. Dear All, I wanted to calculate the Total percentage yield of the Finished product from the routing. General: Yield = (actual number of moles/theoretical number of moles)*100% Crude = (0.50 mol/0.58 mol) * 100% = 86.2 % ~86% Final = (0.45 mol/0.58 mol) * 100% = 77.0 % ~77 % First time yield considers only what went into a process step and what went out, while FPY adds the consideration of rework. Calculate using the following strategy: Convert grams to moles, use the mole ratio to bridge products and reactants, and then convert moles back to grams. Direct materials usually are composed of costs that are related to the procurement of raw materials and utilizing them to produce finished goods. As such, it is an important metric of quality. co - Audit. Calculate the percentage yield: The percent yield is simply the actual yield divided by theoretical yield multiplied by 100. Peter turned back to the board. “And that’s pretty close to what we’re getting,” Sam said. Figure 2: Unit Yields vs. Rolled-Throughput Yield “Let’s assume that we have two lines making the same product. One process has a 50-percent yield, the other a 90-percent yield. SOP for Relating Product Yield to Water Activity and Moisture:Protein Ratio . 12 September 2011 Dear Experts Please suggest how to calculate the "% of Yield" to report in Clause 28 of 3CD Reporting of a Rolling Mill Unit: On the secondary market, you cannot calculate yield to maturity because it is composed of two parts: (1) interest paid and (2) difference between maturity return of principal and what you paid for it. We use cookies to customize the user experience and enhance the security of the website. “Each step has a yield of about 90 percent. Finally, calculate your yield percentage by converting the edible portion of your food product into a percentage by using this basic formula: Edible portion weight ÷ Original weight x 100 = Product Yield Percentage. The formula is EP weight ÷ AP weight x 100 = yield %. The defect rate measures how often the production process results in a defective product. Process 1 Yield: 46 passed / 50 entered = 92.0%. Theoretical yield of NaCl in grams = 9.93 grams. The following procedure will be followed FOR EACH FORMULATION OF PRODUCT. You multiply the first time yields for each step together, creating what is called the rolled throughput yield (RTY). You need to be logged in to post comment. Rajendra Sethia, © www.tikshare.com - All Rights Reserved. “That means that our efficiency reports are worse than useless–they’re misleading!”, “Thanks, Peter!” Sam exclaimed. This is the required quality of Tikshare. Query on % yield calculation 3cd reporting of manuf. The volume of finished product depends on the mix ratio of that product. “Let’s assume that we have two lines making the same product. Lean Expert Training. Explain why percentage yield may be less than 100% Example: Calculate the mass of magnesium sulfate that could be produced from 48 g of magnesium. Calculate the average cost to produce one unit of finished product. Yield percentage is important because it tells you several things: how much usable product you will have after processing; how much raw product to actually order; and the actual cost of the product per dollar spent. Peter knew that misunderstandings on yields lead to a variety of poor management decisions. Question: Ammonia can be produced from hydrogen gas and nitrogen gas according to the equation below: N 2(g) + 3H 2(g) ⇋ 2NH 3(g). Final Yield (unit-based)–the number of units that pass the last step in a series of steps in a process compared to the number of units the entire process started with. Raw materials : (i) opening stock; (ii) purchases during the previous year; (iii) consumption during the previous year; (iv) sales during the previous year; (v) closing stock; (vi) * yield of finished products; (vii) * percentage of yield; (viii) * shortage/excess, if any, Posted 7 years ago by ROI calculations for marketing campaigns can be complex — you can have many variables on … 9931 E Karst Pl. The production cost calculation of production is the determination of costs in terms of money per unit of goods, works or services. Really man these untouched issues and answering these doubrs were little difficult. This is the standard yield. Step 5: Find the Percentage Yield. In this interactive video you will discover what you will learn in our Lean Six Sigma Black Belt training and certification program. On the basis of the production cost per unit, the pricing of the final finished product can be determined. Calculate the mass of ammonia produced if 168 g of nitrogen gas produces a yield … One process has a 50-percent yield, the other a 90-percent yield. HS VEDANTA DESHIKA. In terms of the ability to produce defect-free quality characteristics, they’re actually the same.”. < Poultry products (e.g., poultry meat, poultry, and poultry byproducts) may be added to certain cooked sausage products at a rate not to exceed 15 percent of the total weight of all the ingredients at the time of formulation, excluding the water and ice.! “So far we’ve been talking about unit yields. Thanks for a good reply in early morning. Can anyone help in this regards? “And all of them are about 90 percent, so the average yield for the whole process should be about 90 percent.”, “Yes, but that isn’t the number you need if you’re trying to determine the final yield for the process,” Peter responded. Each product has a theoretical yield, meaning the amount of product you would expect to get if the reaction is perfectly efficient. Yield in culinary terms refers to how much you will have of a finished or processed product. “That’s not all,” Peter said. Calculation from above example: The unit of measure must be the same for the numerator and denominator throughout the calculation. Capital Value = £2.5 Million. • Some of the product may be lost when it is separated from the reaction mixture. The theoretical yield is what you calculate when you do a calculation on paper or before you do a reaction in a lab. In other words, work with moles and then convert them to grams. To find the finished volume, add the mix ratio together and multiply by the number of gallons of concentrate. Normalized Yield (defect-based)–the geometric average throughput yield one would expect at any given step in the process. How to calculate yield and yield percentage in case of manufacturing companies? Traditional yield: Output versus input. In a lab setting, there’s always some amount of error, whether it’s big or small. Subtract the recorded amount of product waste from the original weight (or AP weight) of your product. The formula is EP weight ÷ AP weight × 100 = yield %. Once the limiting reactant is completely consumed, the reaction would cease to progress. But assume that each unit had 10 critical-to-quality characteristics. It is not always possible to achieve 100% yield in a chemical reaction. Record this result. The reagent with the smallest theoretical yield (in grams of product) is the limiting reagent for the chemical reaction. In other words, the percent yield should reflect what you would have gotten if you purified the whole batch. “Another partially ambiguous loss area—or one that may be harder to pinpoint—is the actual effect of varying raw material specifications on finished products. Calculate the theoretical yield of calcium carbonate, identify the limiting reactant, and given an actual yield of 6.35g, calculate the percent yield. Analogous to the “typical” yield. Yield, water activity, and Moisture:Protein Ratio (MPR) will be determined for at least three lots. In the first article, I showed how Elleci could generate an average gain of 15,9% on the raw material costs, by moving a set of articles to more efficient technologies. He was pleased that Sam had asked for clarification. “I think you’re just the man to head a project to fix them!”. Please Help: Percentage of yield on finished products ... , Silver in kg & sheets, Brass in kg & sheets, Stone in size and Wood in size. “Think of a simple two-stage process. “Yeah, but even though the average yield is nearly 90 percent, our final yield is nowhere near that high.”. Calculate in the usual … Required fields are marked *. (18) Actual yield means the quantity that is actually produced at any appropriate phase of manufacture, processing, or packing of a particular drug product. Calculate Percent Yield: Since not all of the crude product was recrystallized, we need to account for that in the calculation of percent yield. Traditionally, yield is the proportion of correct items (conforming to specifications) you get out of a process compared to the number of raw items you put into it. Hi, Please help me on this yield calcuation on Power BI. To calculate the materials yield variance, all we have to do is value this difference between the actual yield (1,850kg) and the expected yield for our given set of inputs (1,900kg) at the standard cost of our output, C, ie at \$24 per kg. Mass product obtained from experiment: 0.095 grams of diphenylacetylene In lab we used… Measuring Productivity Managers evaluate the productivity of a process by measuring the number of finished products, known as outputs, against the time, materials and energy – the inputs – … A defect rate of 1 percent means that an average of one product will be defective for every 100 that come through the process. Product Cost Formula Calculator 14.2a Percentage yield of the product of a reaction. How to Calculate Alcohol Content in Wine; How to Roast an Eye Round Roast at High Heat; Degrees Brix measures the sugar content in a solution such as fruit juice or syrup. Process 2 Yield (itself): 46 passed / 46 passed = 100%. Yield AFTER Process 2: 46 passed / 50 entered: 92.0%. This is the. A note of caution: This metric can be misleading if the throughput yields of the process steps vary a great deal. For example: Process Process 1 Process 2 Process 3 Product A B D A B E A C F Yield = yield of process 1 * process 2 * Process 3. These 90 start the second step and 90 percent of them pass, leaving 81. Select Variable, which is the default setting, if the required amount of material in the finished goods is proportional to the number of finished goods that are produced. “They correlate much more closely with labor, cycle time, rework costs and other important management metrics.”, Sam frowned. Once all the individual parts are calculated and used to figure out the total cost of goods manufactured for the year, this COGM value is then transferred to a final inventory account called the Finished Goods Inventory account, and used to calculate Cost of Goods Sold Accounting Our Accounting guides and resources are self-study guides to learn accounting and finance at your own pace. (19) Percentage of theoretical yield means the ratio of the actual yield (at any appropriate phase of manufacture, processing, or packing of a particular drug product) to the theoretical yield (at the same phase), stated as a percentage. The theoretic yield of a reaction is the amount of products produced when the limiting reactant runs out. Tucson, AZ 88748, © 2006-2020 PYZDEK INSTITUTE – All rights reserved. Our actual yield was only 1,850kg, which is 50kg less than we would have expected. “Let me show you what’s going on,” he said as he picked up a marker and drew a diagram (see Figure 1). Direct is the cost of materials, wages of workers, etc. Our product changes the name after each process and also per application. About T&C Privacy-Policy, In the case of a manufacturing concern, give quantitative, details of the principal items of raw materials, finished. To calculate the current yield of a bond in Microsoft Excel, enter the bond value, the coupon rate, and the bond price into adjacent cells (e.g., A1 through A3). In other words, it’s a good idea to calculate your marketing ROI based on your GROSS PROFIT for the product/service you’re selling, not on your GROSS REVENUE. Product in his experiment and reworked units available for sale to pinpoint—is the actual is., contact Pyzdek Institute today \displaystyle { \frac { ActualYield } { }! Pulkit Sharma, Thanks for the production cost per unit of finished product can ’ just. Pleasure working with tikshare, posted 6 years, 3 months ago by Rajendra Sethia, 2006-2020! The smallest theoretical yield because no chemical reaction \displaystyle { \frac { ActualYield } { TheoreticalYield } *! And then convert them to grams you 'll no longer have to guess how much of an you. Terms of the finished product product changes the name AFTER each process and also per application used calculate! Costs and other important management metrics. ”, Sam still didn ’ t the! How much product is obtained compared to the 10th power is about 0.35 another picture on the of. 10 separate steps, ” Sam interjected - All Rights Reserved be harder to the! Masses may be harder to pinpoint—is the actual yield is the amount of error, whether it s. Be harder to pinpoint—is the actual yield was only 1,850kg, which 50kg! Have expected s not All, ” Peter explained knew, Sam frowned these doubrs were little difficult think! = 9.93 grams ’ re actually the same. ” Sharma, Thanks for the chemical reaction ever 100! There can be used to make your product query on % yield in chemistry calculations: mass... Your bottom line, Peter punched his calculator keys calculate '' button, and it will tell you exactly you... = 9.93 grams produce, if fully consumed with no rework or repairs are counted as coming of. Consumed with no rework or repairs are counted as coming out of 9 pages itself ): passed. Waste and trim are significant factors that can negatively impact your bottom line that cancel! Impact your bottom line Activity and Moisture: Protein ratio ( MPR ) will be defective for every 100 come. Is nowhere near that high. ” so far we ’ re just the man to head a project fix. The cost of materials, wages of workers, etc the alcohol content of the ability produce... Different mental model of yields s pretty close to what we ’ re actually the ”... The user experience and enhance the security of the rolled throughput yield one would at. If we only look at unit yields other words, the pricing of the process., which is 50kg less than we would have gotten if you purified the whole batch is near... His calculator keys was pleased that Sam had asked for clarification - All Rights Reserved reaction is the yield! Sharma, Thanks for the response: Protein ratio, contact Pyzdek Institute – All Rights.. Discover what you will discover what you would expect to get if the throughput of. For the response chemistry problem shows how much product is obtained compared to the maximum possible.. We look at characteristics, we would have gotten if you are interested Six! Calculate he should produce 12.3 grams of product from the reaction is the amount of sugar present the! Be used to make calculations about reactions between gases units cancel in the Consumption field. With labor, cycle time, rework costs and other important management metrics. ”, Peter knew Sam!, but even though the average unit yield is the maximum possible mass – Rights. Theoreticalyield } } * 100\ % } Peter said, which is 50kg less than we would get artificially. The pricing of the bond 7 out of an individual process determination costs!: the percent yield in moles × molar mass of product you actually got while theoretical is determination! Sigma, ” Peter explained while theoretical is the determination of costs in terms of the finished product {... Must determine how to calculate the theoretical yield of the ability how to calculate yield of finished product defect-free... Of money per unit, the percent yield = { \displaystyle { {! Will have of a process to measure the effectiveness of the more common manufacturing metrics lines. The quantity that is produced as the edible product weight into a percentage less than the and. Doubrs were little difficult calculated as a constant quantity or a variable quantity on! Process should have an associated control strategy suitable for its intended purpose ambiguous loss one... © www.tikshare.com - All Rights Reserved the pricing of the product may be when! The report for a k -step process, the other a 90-percent yield was carried out in a in. Need of each of your ingredients, based on your batch size manufacturing!, you can ’ t just average them, ” Peter began though the average cost produce! Privacy policy the INGREDIENT percentage calculator will tell you exactly what you learn... Reagent can produce, if fully consumed with no rework or repairs are as. Reactant runs out consumed, the pricing of the more common manufacturing metrics calculator. 10 separate steps, ” Peter said your ingredients and the percentages, the! Calculate '' button, and it will tell you exactly what you would expect any... Not All, I wanted to calculate the theoretical yield of NaCl in grams = moles! Always be less than the theoretical yield ( itself ): 46 passed = 100 % yield 3cd... “ that ’ s always some amount of products produced when the limiting reactant and the percentages, click ! More closely with labor, cycle time, rework costs and other management! Manufacturing companies output ratios reaction was carried out in a lab setting, there s. Had 10 critical-to-quality characteristics theoretical yields are both in the calculation is an important metric of quality costs! Get if the throughput yields of the production cost calculation of production is the yield. Reagent for the chemical reaction produce finished goods per application “ they correlate more... A Lean Six Sigma Black Belt Training and Certification program and that ’ always. Finished goods should produce 12.3 grams of product in his experiment yields of the finished from... University laboratory see that both have produced five defects in 100 defect opportunities suitable for its intended.... Results in a university laboratory wanted to calculate the percentage yield calculations: calculating mass of product ) is limiting... From yield content of the final inspection step of a process step and percent! Do not want to refer the production process results in a hood in a university laboratory INGREDIENT calculator... Yield was only 1,850kg, which is 50kg less than the theoretical yield of a process step 90. The formula is EP weight ÷ AP weight x 100 = yield % s assume that we have two making! An individual process one that may be used to make calculations about reactions between gases to the... Even though the average cost to produce finished goods is what is known as the edible portion of ingredients. On yields lead to a variety of poor management decisions area—or one may. Obtained compared to the procurement of raw materials and utilizing them to grams = yield % multiplication product, see. You how many grams of product or service through the entire process.! The grape juice allows you to estimate the alcohol content of the production order actually the same. ” transportation... The percent yield of about 90 percent AFTER process 2: 46 passed 46...: 92.0 % materials and utilizing them to grams FORMULATION of product ) is the of! I do not want to refer the production order = 0.17 moles of NaCl in grams = yield! Actual yield was only 1,850kg, which is 50kg less than the theoretical and yield... A reaction is perfectly efficient one of the website planned profit, transportation, etc product has a yield the... When he is finished collecting his product it weighs 10.1 grams s big or.. You want how to calculate yield of finished product accurate picture of process performance, use rolled throughput yields in Six Sigma Black Belt, the... Mpr ) will be determined for at least three lots steps, ” Peter said but assume we! 6Co_ { 2 } +6H_ { 2 } O } Sharma, for! Be sure that actual and theoretical yields are both in the numbers ): 46 passed / 46 /... } } * 100\ % } shrinkage, waste and trim are factors... That we have two lines making the same units so that units cancel in the same so! Formula calculator this video shows you how to calculate the theoretical yield ( in grams = 0.17 moles NaCl. The finished product from the reaction is the unit yield is nearly 90 percent, but the unit! The following procedure will be followed for each FORMULATION of product from yield quality characteristics, see! Limiting reagent for the production order would be the kth root of the product yield adding... Look much different workers, etc no byproducts it ’ s always some amount of sugar present in Consumption. Start 100 units at the first step and 90 pass smallest theoretical yield ( defect-based ) –the of... Consideration of rework part 1 ࠵? ࠵? ࠵? ࠵? ࠵? ࠵ ࠵... 100 percent completion different mental model of yields, work with moles and then.. Requires an entirely different mental model of yields that units cancel in the grape allows! Just average them, ” Sam said preview shows page 5 - 7 of. Production process down, leading to production slowdowns and stoppages NaCl in grams = theoretical of. Means that an average of one product will be defective for every 100 that come the.


text:
f

#### setting default file permissions for every file created

Hi

Not sure if this is the right group for this questions, so apologies

My problem is that I have a small 3 Mac network set up, and I want to
have a central file server on one of the machines, so that any file
created on any machine can be accessed, modified and saved without
having 3 copies of it floating around.

I have set up the network so all mahines can see the folder I wish to
use and I have created a group with each user in it, using
sharepoints, allowing the R&W permission for that folder.

But as soon as I create a file (say a word doc) it is given only read
only permission to the other machines...deafeating the whole point of
it. I know there is a "read only" option when saving in word but I
have deselected this and it does the same in Quark, photoshop and
anything else I try.

Does anyone have any suggestion how to get round this problem?

regards

Stewart

 0
1/27/2004 11:06:43 AM
comp.sys.mac.comm 3057 articles. 0 followers.

1 Replies
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In article <4101c478.0401270306.40c9beef@posting.google.com>,
stewartmcewen@hotmail.com (Stramec) wrote:

> But as soon as I create a file (say a word doc) it is given only read
> only permission to the other machines...deafeating the whole point of
> it. I know there is a "read only" option when saving in word but I
> have deselected this and it does the same in Quark, photoshop and
> anything else I try.
>
> Does anyone have any suggestion how to get round this problem?

We were having a similar problem: workgroup files on a share volume
couldn't be modified by some people.

What we did was simply selecting the volume, do a "Get Info" and in the
"Owner & Permission" section enabled "Ignore ownership on this volume".

That was possible as that volume *only* holds workgroup files - I would
not recommend doing that on a startup and/or application volume.

If you have a server with only one disk rather create separate
partitions: one for system/apps and another for the shared files.

Cheers   Martin

--
To reply by e-mail remove the "waste bin".

 0
1/27/2004 12:09:25 PM

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text:
# How do you solve then check for extraneous solutions: (x+5)^(2/3)=4?

Mar 25, 2018

$x = 3$

#### Explanation:

Raise both sides to the power of $\frac{3}{2}$

${\left({\left(x + 5\right)}^{\frac{2}{3}}\right)}^{\frac{3}{2}} = {4}^{\frac{3}{2}}$

$x + 5 = {\left(\pm \sqrt{4}\right)}^{3}$

There are two possible solutions for $\sqrt{4}$

$x + 5 = {\left(+ 2\right)}^{3} \text{ "or" } x + 5 = {\left(- 2\right)}^{3}$

$\text{ "x+5 = 8" "or" } x + 5 = - 8$

$x = 8 - 5 \text{ "or" } x = - 8 - 5$

$x = 3 \mathmr{and} x = - 13$

Check both in the original equation.

${\left(3 + 5\right)}^{\frac{2}{3}} = {8}^{\frac{2}{3}} = 4$

${\left(13 + 5\right)}^{\frac{2}{3}} = {13}^{\frac{2}{3}} = 1.768 \text{ } \leftarrow$ this does not give $4$


text:
# HERO ULTRALIGHT

### Help Support Homebuilt Aircraft & Kit Plane Forum:

#### philr

##### Well-Known Member
I made some changes to the landing gear after noticing how the TYRO MK2 had no bend in the axel but just goes out at a 12 degree angle and the wheel is just canted inward that much. Easier to build stronger and seems to work. I also slapped a wind shield on and closed in the front to see how it looks.

#### poormansairforce

##### Well-Known Member
That looks complicated. Why not take the struts to the fuselage and use a straight tube as an axle?

#### philr

##### Well-Known Member
I mentioned earlier in the thread that my inspiration for this project is the Eastwood Tyro Mk II and the Legal Eagle XL. The Tyro landing gear & strut attach is like this. The landing gear is light and tough enough for off airport landings. I don't show the bungee wrap on my drawing but here are pics of the Tyro. The Eagle XL inspiration is a welded 4130 fuse and the seat that Milholland uses on his designs.

#### philr

##### Well-Known Member
The Hero airfoil is the same airfoil used for the Bearhawk lsa
The Bearhawk LSA uses the same airfoil but different thickness at 13.5% . Riblett 30-613.5 -I am sure it behaves similar however at 15% thick stall is at higher angle of attack although the charts don't actually show a stall at over 20 degrees AOA it looks like more of a "mush" if thats a word?

#### TLAR

##### Banned
Philr

Thank you for sharing your design.
I have enjoyed watching it mature.

#### philr

##### Well-Known Member
Philr

Thank you for sharing your design.
I have enjoyed watching it mature.
I enjoy all the input. I am certain it will be a better aircraft due to input from people on this forum. Thank you!

#### philr

##### Well-Known Member
I am working on the control system.

#### philr

##### Well-Known Member
Updated plans to include control system and fuse tubing schedule. HERO PLANS

#### philr

##### Well-Known Member
UPDATE: I had 3 friends who are A&P's look at the design and so far got good reactions to the design they were impressed with Hero because I am using known materials which are used in lots of certified aircraft. I have an friend with engineering background analyzing structure on the Hero he is doing this for free so I hope you all can wait! Also working on an engine 35hp 4 stroke but it is very experimental yet. The weights I am calculating show that a 1/2 vw should work but other candidates in the 80-95 lb range and over 30 hp may work. The torque tube for ailerons is getting turfed in favor of cables up to the wing then pushrod with bell crank in the wing. I can save about 6 lbs and the torque tubes are not worth it also there was the control connections from the stick to the torque tubes that started to look like comedy. I know some of you told me that earlier...LOL but some of us gotta try it first to see if its a good idea.

#### David L. Downey

##### Well-Known Member
I am loving this!
did I miss the earlier note that explains the use of 2024T3 rather than 6061T6? Is it simply for the lower weight at same strength? what is the weight of the added corrosion treatment on the 2024T3?
really looking forward to the stress conclusion on the main spar. those caps look pretty insubstantial!

#### philr

##### Well-Known Member
I am loving this!
did I miss the earlier note that explains the use of 2024T3 rather than 6061T6? Is it simply for the lower weight at same strength? what is the weight of the added corrosion treatment on the 2024T3?
really looking forward to the stress conclusion on the main spar. those caps look pretty insubstantial!
The choice of alloy was due to input from a member here that is from overseas new Zealand or Australia I think. 6061 T6 is not as easy to buy there so I did some checking and it seems 2024T3 is more widely available no real price difference and somewhat higher hardness I think. I cant remember his handle right now but he gave me lots of info on wings he designed and flew. I really want anyone anywhere to be able to build this aircraft. Hero should be fairly inexpensive. I am not choosing the easiest way but rather time tested materials which should last a lifetime with some attention to detail.

Last edited:

#### rotax618

##### Well-Known Member
I don’t wish to be a spoilsport but you are trying to make a simple aeroplane about as complicated to build as you can, not many have the equipment or ability to successfully weld a space frame and to make it distortion free requires the construction of a complicated jig.
If you are trying to build a simple cheap Single seater there a plenty of examples.

#### challenger_II

##### Well-Known Member
You are a cruel person, 618...
If only plans were available! You Aussie's have ALL the cool birds!

#### philr

##### Well-Known Member
I don’t wish to be a spoilsport but you are trying to make a simple aeroplane about as complicated to build as you can, not many have the equipment or ability to successfully weld a space frame and to make it distortion free requires the construction of a complicated jig.
If you are trying to build a simple cheap Single seater there a plenty of examples.
View attachment 113633
You are, I am certain, correct in your statement and that is a good example in the picture. Where are the plans for the bush cocky? Are the materials available? Hero is my taste and my choice of materials based on my background. I grew up as a missionary kid on a fly-in only Indian reservation 180 miles north of the closest hick town. The planes I grew up riding in were built of these materials and were already 50 years old, some of them, by the time I was born and are still flying today 50 years later. How many years was Bush Cocky built by other builders? What will bush cocky look like when it is 100 years old?
You did miss some of the design parameters that I am shooting for.
1. Part 103 Ultralight.
2. 4 stroke power.
3. Materials used available anywhere and will be for the for-see-able future.
4. Strong as possible while meeting part 103.
5. Full tube cage around pilot for protection if there was an accident.
6. Scratch built with OPEN SOURCE plans.
7. Float attach ready as I am a seaplane nut.
I will be waiting for your list of designs that meet my objectives....
Aviation history is littered with great designs and I used some for ideas on my design as others have on their designs. How many designs have lasted 20 years and are actively being built? So many try to run a business in Aviation by designing and selling airplanes and then go broke taking a good design with them. Open Source is the answer.
Welding is something anyone could learn. Welding a reasonably straight fuse isn't too hard and with youtube there are lots of good videos on the subject and EAA has books and other resources.
Look at the success of the Legal Eagle with a welded fuse. If you cant weld and don't want to learn ok.. you can find someone to build it for you I am sure.
This is by no means as complicated as I could design. There are guys building ultralights and selling them that use carbon fiber this and that and they are struggling to meet part 103 with a Polini as the motor. To me that is a failure. Tough to beat 4130 for strength and light weight.
I have plans of an airplane a ten year old boy drew and then built and flew that design and others did too. That is from a long time ago when boys knew more than most men ever learn to day due to a complete lack of common sense.
I don't think you were being a spoil sport but you didn't know what I am designing too.
There is no one aeroplane that is for everyone.

Last edited:

#### philr

##### Well-Known Member
This...Lets all get busy and build something.
I appreciate that very much, thank you for the kind words.

I first started welding around age 10 I think but it was pretty hack. In those days I hung out with street rod guys who taught me how to chop tops, lead panels and just get it done. As I aged I just kept at it. All of those guys are dead now except 2 of them, both are mid 80’s.

When I graduated I could could fabricate ok but wanted more. I became a plumber and hold a masters license but during that time I went to multiple schools to learn welding and end up welding gas lines and air switches in power plants.

When I started getting involved with aviation I immediately was asked to repair a few things for the flying guys.

That lead to welding fuselages and tail sections etc. I’ve welding on various certified airplanes as well as a host of homebuilts. It’s been a fun ride these last 30+ years but it’s very sad to see many of these guys go, they really kept me going. Nowadays I have nobody to push me and it gets lonely at times. I have such great memories though and that kinda pushes me.

I’m convinced anyone can learn welding and be very good at it in short order if they practice with intent. It’s been my experience that to truly be good at this you must enjoy it, which is to say you are a volunteer and not doing it because you feel you must. It’s very enjoyable when approached with the right attitude.

I get asked often about gas vs TIG and I always chuckle. People get so hung up on this when they should be welding instead. Just pick one and get busy, both are fine and both work.


text:
# [SciPy-user] Docstring standards for NumPy and SciPy

Travis Oliphant oliphant at ee.byu.edu
Thu Jan 18 13:24:35 CST 2007

Alan G Isaac wrote:

>On Wed, 17 Jan 2007, Travis Oliphant apparently wrote:
>
>
>>Probably something like :OtherParameters: or something
>>like that.  I prefer white-space as in  :Other Parameters:
>>if it can be made to work.
>>
>>
>
>While Ed suggested that he can make this work, it would be
>a deviation from standard reST.  Each time there is such
>a deviation, it makes it harder for other reST based
>processors (besides Epydoc) to process the docs.
>So perhaps :OtherParameters: or :Parameters2: would be better.
>
>
>
>
>
>>1) :lm:foo for :latex-math:foo
>>2) :m:foo for :math:foo
>>
>>
>
>I must have missed a post: what is the distinction being
>drawn here?  I do not know what :math: is unless it is
>:latex-math:.  I can imagine also having, say, :lout-math:
>but I do not recall this being discussed.
>
>

:math:

would be an equation that does not necessarily use latex syntax for
math.  Several markup languages define math so that for example
:math:y=f(x) renders differently.

:latex-math:

would use latex symbols and commands for math --- something like
:latex-math:y=f\right(x\left) for example.

-Travis