Would a smaller re-entry vehicle better handle very high re-entry speeds?

Question

"Inspiration Mars" has the idea to use a free return trajectory for a crew of two rounding Mars. While attractive in some ways, this free return trajectory has the disadvantage of ending up with a very high re-entry speed as it comes back to Earth's atmosphere. Heavy heat shields and/or lots of fuel for breaking rockets counterbalances some of the advantages.

It is often (always?) suggested to use adaptations of capsules like Orion (NASA) or Dragon (SpaceX) as re-entry vehicles. But they are greatly overdimensioned for a crew of two using it for a few hours as they approach Earth after having discarded the rest of their spaceship. I'm thinking of a claustrophobic cage like Gemini. They wouldn't need to operate anything. They would need none or minimal life support systems except their space suites.

Wouldn't these be some great advantages of a tiny REV?:

1) Smaller surface area of the capsule needs a smaller heat shield. But maybe the physics involved is not that simple?

2) Lower mass of capsule and heat shield makes the braking rockets and also the parachutes more efficient in slowing down the speed.

3) Tiny crewed re-entry vehicles were used about 50 years ago. Making them smaller than those used and planned today should make the challenge of high speed re-entry easier, even if a capsule design has to be made from scratch.

And finally, would a fast re-entry vehicle have any more generally useful application?

I've looked through some of the student contributions in the Mars Society / Inspiration Mars contest, so I feel like a rocket scientist now! :p Link (posted on marssociety.org Mar 28, 2014, 3:48 PM by M Stoltz): http://www.marssociety.org/home/press/announcements/marssocietypostsinspirationmarsstudentdesignreportsonline

Answer 1

Regardless of the size, unless someone is being foolish, the vehicle will be designed to handle the reentry speeds. So a small one won't handle them "better" than a large one.

However you are correct that it is easier, and will take much less mass for a small one to handle the speeds and other landing responsibilities than a large one.

If it has already been accepted that there will be a separate habitation space from the entry vehicle, and for Inspiration Mars it has, then it makes sense to make the entry vehicle as small as possible for the crew to be able to fit inside and to support the crew independently for an hour, if that. That is basically the philosophy of the Soyuz spacecraft, which unlike Apollo had a separate habitation space.

Answer 2

Ballistic Coefficient is an important quantity for looking at re-entry. Ballistic coefficient scales with mass/cross sectional area.

Increase a shape's dimensions by a factor of r and it's cross sectional surface area will increase by r^2 and its volume by r^3. So ballistic coefficient becomes less as size increases.

Here's a pic of a range of objects all having the same ballistic co-efficient:

So yes, it's easier to have a more favorable ballistic coefficient for small payloads.

Answer 3

There is a weird project currently being studied to "land" probes on Mars without parachute or retro-rockets or whatelse: probes will be so thin and large that they will just slowly fall down like paper sheets without getting damaged. http://www.space.com/25000-planetary-exploration-flat-landers-tech-nasa.html

This is possible because what is needed for a "soft landing" is a small vertical speed. An object left in free-fall in atmosphere accelerates up to "terminal velocity", when air drag force becomes as high as gravitational force, so no more force results applied to the body, hence no acceleration, hence no speed variation.

Air drag force is $F= \frac 1 2 \rho C_d A v^2$, where $\rho=$ air density, $C_d$=Air Drag coefficient and A=cross-section area . The larger is the cross section area, the higher will be air drag force.

Gravitational force (accelerating object): $F=mg$

Air drag force (braking object): $F=-\frac 1 2 \rho C_d A v^2$

Hence maximum achievable speed for a free-falling object is: $v_t=\sqrt \frac {mg}{\frac 1 2 \rho C_d A}$

If you can tune m, $C_d$ and A to achieve a low terminal velocity (5-10 m/s), you get a soft landing.

So, rather than "smaller" vehicle, you need a "larger" vehicle

Answer 4

In regards to point two, if a vehicle is smaller it means it will be a lot lighter. Lighter vehicles mean smaller re-entry parachutes, which also means that you have a reduction in carry weight when taking off.

The bigger the vehicle the bigger the canopy will have to be. This also means the bigger the deployment drogue will have to be as well as the thickness of the used suspension materials which will connect the vehicle to the chute.

The lighter the weight of the capsule, the smaller the parachute will have to be.

See my other answer here for more information on parachutes.

Answer 5

I think your point 1 isn't phrased as well as it could be. What I think you mean is "cross-sectional area", not "surface area".

If you are using a material with reasonable heat transmission (i.e. not ceramic blocks, see below) having a larger surface area allows you to spread the thermal load more effectively. This is contrasted by having a larger cross-sectional area which will increase the thermal loading in the form of drag/friction/shockwave heating/etc. Thus larger surface area is beneficial, and a larger cross-sectional area is not.

Note that what I'm referring to is the "heat sink" method of dealing with reentry heat. This technique is not suited for all craft. The space shuttle, for instance, did not use it, instead opting to protect against convective heat transfer. The shuttle can be thought of as a giant thermos, making heat transfer to the skin difficult, whereas the heatsink method can be thought of as absorbing all of the heat to radiate it back over time (once the heat source is removed).

Interesting thermodynamics point: conductive transfer is how friction is applied, but with re-entry shockwaves you can design it so that ones heat load is nearly all convective... which means an air gap is effectively acting as your first layer of insulation.