Heat-shield for a Mach 30 missile at 10km for 10 seconds?

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Treva31
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Using an ablative carbon-carbon heat-shield, what thickness would be used up?
Or might a ceramic insulator be able to handle it?
What would happen if the nose was solid aluminium?How can this be calculated?
What information do I need to figure this out?
 
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This problem is substantially more difficult than I suspect you realize. It can't just be calculated using pencil and paper. In fact, heat shielding is even a challenge for the people who do this for a living (NASA, Air Force, etc.) and usually involves some very rough calculations performed using CFD and then adding a pretty hefty factor of safety to account for all of the variables that we still don't fully understand such as boundary-layer transition, which can increase the local rate of heat transfer by an order of magnitude.
 
I understand that its very complicated and inaccurate.
But what information would I need to know in order to get an approximate answer?
Lets say just for the ablation scenario?
 
You would need all the ambient conditions that come along with altitude (temperature, pressure, density). You would need to know the composition of the gas (is it "air"? is it carbon dioxide like on Mars? etc.). You would need to know the shape of the vehicle. You would need to know the character of the surface of said vehicle (i.e. how rough is it and does it have any sort of protrusions and what is it made of). You would need to know information about how all of the components of the gas react with each other when they become ionized from the heat at those speeds.

Generally, not all of these things are necessarily taken into account every time someone designs a vehicle because it is obviously a very complicated process that would require magnanimous amounts of computer time to solve, and that is even assuming that the computer models would be correct. It is difficult to actually test such a thing as well, so really there are generally just a bunch of simplifying assumptions that are made (e.g. ignore chemistry) and a factor of safety is added. In reality, most heat shields are pretty significantly over-designed because of this.
 
Perhaps it would be possible to calculate the energy needed to move the air away from the missile's path.
Then, by conservation of energy, no more material should be needed than what can be melted or vaporized with this amount of energy (aluminum would melt, ceramics probably vaporize).
Alternatively you can guess the energy, if you know how much fuel does the missile carry.
 
Have a look on the NASA site : https://www.nasa.gov/

There is a lot of information on there about heat shields for Apollo and the Space Shuttle .

The whole site is full of fascinating information about space exploration .
 
This is a subject that will be a hard nut to crack for a few reasons:

1. As already mentioned, the physics is very complex.
2. Much of the critical data for extreme hypersonic flight is likely to be classified due to its military value.
3. Mach 30 is just damn fast.

The more likely solution will probably be some form of active thermal management augmenting the coating material of the vehicle. That is, using the hydrogen fuel as skin coolant and/or creating an artificial boundary layer of air to act as a thermal blanket.

Both techniques will complicate the calculation of material ablation because we are now adding additional parameters to the equation.

This is both good news and bad news. The bad news is that getting a realistic answer may be difficult to impossible. The good news is that you might get away with a good educated guess because no one would be able to seriously challenge your numbers, so the suspension of disbelief is not threatened.