Pardon me for the stupid question, but how is bringing the speed down to 0 milliseconds before landing by firing the rocket thrusters different from just letting the capsule hit the ground? I thought the thrusters were there to make the passengers not feel the inertia due to sudden arrest of speed from 16-17mph to 0mph. Firing the thrusters milliseconds before landing seems to have the same effect as just letting the capsule hit the ground? Or is it to protect the capsule itself?
I'm a bit rusty on my physics, but the general idea is that with both methods the total impulse (force over a time interval) is the same. The capsule goes from 16mph to 0mph.
But, if you let the ground stop you, you end up with all of the energy transfer in a few milliseconds. Because the time is so short, the force spikes to crazy high levels. This breaks equipment and people. The rockets firing spread out that force over a longer period of time.
For example (all numbers made up):
Time the ground takes to stop you: 25ms
Time rockets fire before touchdown: 100ms
Landing capsule weight: 2000kg
Impulse needed to stop capsule: 7.15264m/s * 2000kg = 14300Ns
Assuming in both cases the force is evenly applied over the time period...
Force from the ground stopping you: 14300Ns / 25ms = 572,000N
Force from the rockets + the ground: 14300Ns / (100ms + 25ms) = 115,000N
