Really silly question (atmos re-entry)

[alex04]

Regarding atmospheric re-entry,

when i was younger i used to wonder why space-craft couldn't simply fire the engines to reduce the re-entry speed to make it a less dangerous affair - i arrived at the conclusion that maybe there wouldn't be enough fuel for this.

However in the Apollo 13 mission (yes, from watching the movie ;D) after the explosion they briefly considered the option of doing a direct abort with the main engine, which i think would require considerably more fuel - bearing in mind though that i'm not aware of the velocity of the spacecraft at this time).

So what's the real reason why they don't simply fire the engine to reduce the re-entry speed? (i'm guessing there may be a number of complicated reasons i'm not aware of).

[Count Zero]

You got it right on your first guess: Not enough fuel. The mass of the braking fuel (and the fuel tanks, and the structure that would support them) would be much more than the mass of a heat shield. Depending on how much you want to slow down, the fuel & tankage for braking might mass more than the spacecraft you are trying to slow down!

The situation discussed in "Apollo 13" had nothing to do with atmospheric re-entry. The accident occured when they were a bit more than halfway to the Moon (>100,000 miles above the atmosphere) and still out-bound at over a mile-per-second. The fastest way to return to Earth would be to kill this outward velocity and fall back to Earth. The LM rockets did not have enough fuel to do this. The SPS engine in the service module did, but since it was in the damaged section, they did not want to use it. Instead, they used the LM descent engine to adjust the outbound trajectory so that they would pass by the Moon at the correct distance so that the Moon's gravity would sling them around on a course that would take them back to Earth. It took longer (which stretched their limited resources) , but was safer than trying to use the SPS engine.

[alex04]

I realise that the situations were totally different c.zero, but i understand now that basically the point is - that the amount of fuel required to an about-face towards earth is negligible, compared with trying to slowing capsule right down for re-entry

thanks

[Bob B.]

Using the atmosphere to slow the spacecraft is a very efficient way of doing it. Like you said, it takes a tremendous amount of propellant to decelerate the craft propulsively. Instead the craft is slowed just enough to drop it into the atmosphere and then drag does the rest. Furthermore, the capsule still needs to drop through the atmosphere even if slowed by the engines, so that aspect isn’t removed no matter what you do. In fact there is actually a higher peak g-load if the capsule drops at a steeper angle from a slower velocity. For instance the suborbital Mercury flights experienced a peak deceleration of something like 11-12g while the orbital flights peaked at about 7-8g, though the orbital flights experienced high g-loads for a longer period of time. Coming in fast allows more deceleration to occur while moving mostly horizontally through the less dense upper atmosphere. By coming in slow the craft experiences very little deceleration until it reaches denser atmosphere, at which time it experiences a brief but very intense g-load.

Regarding Apollo 13, it is my understanding there were some abort modes that allowed for a direct abort – i.e. burning the service propulsion engine to essentially reverse the spacecraft direction and bring it straight back to Earth. I haven’t studied this part of Apollo, but I image this was possible only during a window of time when the spacecraft wasn’t moving very fast. Doing this doesn’t change the method of reentry once the spacecraft gets back to Earth.

[Bob B.]

alex04 said:

- that the amount of fuel required to an about-face towards earth is negligible, compared with trying to slowing capsule right down for re-entry

It is certainly not negligible but it is smaller than the velocity in low Earth orbit. The SPS had the ability to change the CSM's velocity 2.8 km/s. In low orbit the spacecraft is moving about 7.8 km/s and is accelerated to nearly 11 km/s to send it to the Moon. After injection into the translunar trajectory the spacecraft immediately begins to slow down as it moves away from Earth and doesn't start to speed up again until it gets very close to the Moon. There is a point in the middle when the 2.8 km/s delta-v of the engine is enough to do a direct abort. Getting this 2.8 km/s required that the the CSM be about 60% propellant.

[ajv]

There were a number of pre-planned return to Earth points and the crew were sent pre-advisory data to allow a return in the case of an emergency and a loss of communications.

The A15 flight journal has some examples. See page 2-15 of the Apollo 15 flight plan. The first was TLI+90 using the SPS timed for 004:19:57ish for a delta-v of 1.506 km/s. LO+8 (timed for 008:00:00) had a delta-v of 1.852 km/s using the SPS in Program 37.

[alex04]

bob said:

Furthermore, the capsule still needs to drop through the atmosphere even if slowed by the engines, so that aspect isn’t removed no matter what you do. In fact there is actually a higher peak g-load if the capsule drops at a steeper angle from a slower velocity.

to ask a very hypothetic (and naive!) question,

what if you managed to get the spacecraft to zero velocity, and then allowed for a free-fall?


thanks for the comments guys, interesting stuff

[Count Zero]

That's essentially what Apollo did. The spacecraft dropped to Earth from an altitude of 230,000 miles. By the time it hit the atmosphere, the Earth's gravity had accellerated it to 7 miles-per-second. As Bob pointed out, you don't want to drop straight down into the atmosphere: The g-load is high, and heating can stress the heat shield beyond what it was designed for and burn-up the spacecraft. Thus there is a horizontal component to the "long fall" that allows the spacecraft to hit the atmosphere at an angle to reduce the g- and thermal-loads.

[alex04]

Sorry Count Zero -

what i meant was - if the craft was released from zero velocity - from a slightly conservative altitude - say 300kms

Im just entertaining the absurd notion in my head that if it were possible to brake the craft to zero velocity @ say 300kms - maybe it would survive a direct freefall? (with chutes of course!)

[Bob B.]

alex04 said:

Im just entertaining the absurd notion in my head that if it were possible to brake the craft to zero velocity @ say 300kms - maybe it would survive a direct freefall? (with chutes of course!)

My first impression is that the spacecraft would fall essentially unimpeded for the first couple hundred kilometers and then the deceleration would come on very rapidly with a intense and but shorted lived peak.

To verify I roughed out a simple simulation - didn't have time to get really sophisticated but it ought give us a pretty good idea. There is almost no deceleration at all until the spacecraft has fallen over 200 km. The deceleration doesn't reach 0.01g until an altitude of about 80 km, at which time the velocity is over 2,000 m/s. The spacecraft continues to build speed for another 17 seconds or so until it drops below 45 km. It then begins to decelerate very rapidly reaching a peak of over 15g at an altitude of about 21 km. The g-force then subsides as quickly as it developed. The deceleration exceeds 2g for a period of about 30 seconds, 4g for about 20 seconds, and 10g for about 10 seconds. By the time the capsule reaches 10 km altitude it has slowed to about 200 m/s.

[PhantomWolf]

Just wanted to point out that with Apollo 13 they were still on the way to the moon, so the SPS not been fired. Bob pointed out that slowing down to a slow re-entry would take up 60% of it's fuel, but most of the fuel was to be used for Lunar Orbit entry, and Lunar Orbit exit. To have added an extra 70% or more in (you need more than 60% because you have more mass to decelerate into lunar orbit and get back out) would have meant bigger rockets to get the stack into space and to the moon. A heat shield wins hands down.

[Bob B.]

phantomwolf said:

Bob pointed out that slowing down to a slow re-entry would take up 60% of it's fuel

That's not exactly what I meant. Approximately 60% of the CSM's total mass when fully fueled is the mass of the SPS propellant. If all of this propellant is burned at one time, the CSM's velocity change will be 2.8 km/s. As you say, virtually all of this propellant was available for abort while on the way to the Moon (at most a small amount may be used for a course correction).

phantomwolf said:

To have added an extra 70% or more in (you need more than 60% because you have more mass to decelerate into lunar orbit and get back out) would have meant bigger rockets to get the stack into space and to the moon.

This is an important point. Each increment of velocity requires more propellant than the previous increment. If it takes X amount of propellant to reach Y velocity, it takes >2X propellant to reach 2Y velocity.

The CSM had a mass of about 30 metric tons, of which about 18 tons was propellant and 12 tons the dry spacecraft. This gives us a mass ratio of 2.5, which is the total fuelled mass divided by the dry mass, 30/12 = 2.5. As I said earlier, this mass ratio produced a velocity change (delta-v) of 2.8 km/s. (The amount of delta-v depends not only on the mass ratio but also on the type of propellant and the engine design. The numbers here assumes the Apollo SPS.)

Let's say you want to double the spacecraft delta-v to 5.6 m/s. This requires a mass ratio of about 6.25, or if the dry mass is 12 tons, the total mass is 75 tons. But we're not done yet... with more propellant we need bigger and heavier propellant tanks. Let's say the dry mass swells to 16 tons, the total mass is now 100 tons (84 tons of propellant). We've more than tripled the mass of the spacecraft to double the delta-v. Now consider that to get these extra 70 tons of spacecraft and propellant into space requires a very large increase in the size of the launch vehicle.

As you can see, a mere doubling of the delta-v has a dramatic impact on the propellant mass, the size of the spacecraft, and the size of the launch vehicle. Deorbiting a spacecraft doesn’t require much delta-v at all, typically about 0.1 km/s. If you were to halt a spacecraft’s orbital velocity so that is drops straight down, you’d need a delta-v of 7.8 km/s. You’re not doubling the delta-v, you’re increasing it 78 times! Just imagine what that does to the size of your spacecraft!