Aerospike nosecones have a couple of big benefits which, to fully appreciate, I'd need to give a little background on.
At the risk of dating myself, "Sherman, set the WABAC machine to the 1950s":
The United States had a problem. It was trying to develop a missile with a range of 1,000 miles based on the work of Wernher von Braun and a number of other ...
It was charred by the center core after separation:
(Source: SpaceX FH launch webcast)
Looking at it I would expect one side to be charred too but it may not be - the nose cone is afaik composite (same as the interstage) and not metal.
You'll notice it is used on submarine launched ICBMs.
Blunt noses are very efficient for the missile to get out of water (and are shorter than long, profiled ones, which helps with submarine diameter), but aren't great in atmosphere; hence the deployable aerospike to make them efficient in both media.
As rockets get larger, the importance of drag relative to mass decreases (drag runs generally proportional to cross section and surface area while mass runs generally proportional to volume). Hence big rockets tend to have less pointy payload fairings, which provide more useful volume by mass, as Hobbes' answer shows.
Qu8k was a small rocket developed with ...
Blunted noses, especially in the case of the Shuttle Orbiter, are a thermal consideration as well. To put it simply, when a vehicle travels at supersonic speeds, there is a shockwave produced by the nose “because the air wouldn’t otherwise get out of the way fast enough”. This wave produces a large component of total drag, especially at hypersonic (Mach > 5) ...
Orbital rockets generally don't have such sharp noses. Here's an Ariane 5 as an example:
You can see there's a large radius on the tip. Eyeballing from a scale model I have handy, I'd say that radius is about 0.5 m.
The Falcon 9 fairing has a large radius too:
The Apollo LAS had a sphere embedded in the tip.
The nose design with the lowest drag seems ...
According to this webpage, under the payload shroud were the airlock, the multiple docking adapter, and the Apollo telescope mount. The latter was folded in front of them but swung to the side on orbit entry. The Saturn Instrumentation Unit (I.U.) was also above the third stage.
Dragon’s landing parachute is stowed roughly in the nose cone hinge area, and this leads me to believe the nose cone has to open for the chute to deploy.
That belief is incorrect. Other than both being installed near the top of the vehicle, the parachutes and the nose cone have nothing to do with each other.
In normal operations, I believe the nose cone is ...
Yes and no. If it failed to close, it would damage the systems somewhat. There is a way to manually eject the nose cone, which is what would be done in such a situation. Presumably this would limit reuse and increase the risk, but not ultimately be as risky as having an unclosed nose cone. Note that Crew Dragon reentering with no nose cone is pretty similar ...