Apollo 15: What if two parachutes had failed, and how fast?

I saw something about this today:

Apollo 15 made splashdown with two of the three chutes deployed, and the astronauts were none the worse for wear.

I’ll assume that if no chutes had deployed, that very likely would not have been survivable, but what if only one had? About how fast would it (or any other capsule) have hit the water?

The Apollo capsules were designed for a two-parachute splashdown, the 3rd chute was a safety margin. no chutes deployed would mean a 200 mph splashdown (un-survivable). One chute deployed would have slowed it down enough for maybe survive but you could probably expect severe injuries at least. How fast they would hit and at what angle/rotation with just one chute would depend on a lot of factors - which of the three chutes deployed, partial deployment of any of the other two, spin of the capsule due to instability, etc.

If only a single parachute fully deployed, that would have been a bad deal.

On Apollo 12 they had all 3 deploy just fine, but the pendulum swing of the command module and wave action on the ocean surface coincided “just so” and they smacked pretty hard. Some equipment was dislodged and smacked Al Bean in the head.

Two chutes is 32 feet per second and three chutes is 28 feet per second. I’m unsure of the math to determine the rate with just one chute.

Aero drag is proportional to the square of speed. So if you cut the drag in half (by going from two chutes deployed to just one chute deployed), then the square of your speed gets doubled - which means your speed goes up by the square root of 2, i.e. multiply the 32 fps by 1.414; you’d expect them to be coming down at about 45 fps, or about 30 MPH. that’s gonna be a pretty hard impact.

Thanks for doing the math. But is 30 MPH anything that the craft and crew restraints couldn’t handle, especially when hitting something as pliant as water? I wouldn’t want to try it, but it doesn’t sound too extreme to me.

I’m doing the math on my phone in a hotel room right now, so no guarantees. I looked up the following:

Apollo command module diameter, 12 feet 10 inches.

Command module weight, 5557 kg.

So for 30 mph, you calculate the RAM pressure from the water on the bottom of the capsule as it splashes down. Multiply that pressure by the area of the bottom of the capsule, and you end up with the force of the water on the bottom of the capsule as it splashes down. Divide that force by the mass of the capsule, and you end up with the number of g’s experienced by the capsule at the moment of splashdown. After all that, I ended up with 20 g’s. I don’t think that would have been a problem for the astronauts themselves, as they were lying on their backs during reentry and splashdown, a good position for tolerating g loads. But since that splashdown speed is about 1.6 times the speed that they experienced with three parachutes, that means the splashdown deceleration with one parachute would have been about 2.56 times as much as with three parachutes. Knowing how tight the safety factors are on spacecraft, it seems likely that this would have bent bent or broken some things, for example the seats or slings that the astronauts were lying in, and possibly also the structure of the command module itself.

Is water pliant at high speeds? There’s a reason divers try to hit with a pointy formation. Full on belly flop hurts. And the command module was designed to land with the biggest, flattest part hitting the water.

Not a scientist; just asking?

Hitting water straight on isn’t hitting anything all that pliant. Famously in one of the water drop tests the entire bottom of the capsule catastrophically failed - which in real life would have been a very bad day. The structure was redesigned.

Worryingly, all I can find is mention of single canopy failure tests, and an implication that the capsule structure was only rated for a single failure on impact. So rather than worry about injury to the astronauts, one might be more concerned that the capsule might have almost instantly sunk.

The couches had crush can shock absorbers that were meant to limit Z direction impact to 20g.

There were also a heap of tests done to see how things would go if they landed on land. Which was a real concern if they aborted in the first 40 seconds. But I have a feeling they assumed at worst a single canopy failure.

Generally I get the feeling that anything that didn’t destroy the capsule was expected to be survivable, but not necessarily injury free. Once the capsule is damaged you buy into the problem of a significant number of toxic chemicals- hypergolics etc, as well as the capsule sinking.

Other countries land on land. How do they pull that off?

It’s a really hard landing, is my understanding.

Could the balloons that were in the capsule to right it if it landed sideways have prevented sinking?

It isn’t that much more difficult. Some form of retro-rocket is a common design. They fire just before impact.

Both Gemini and Space-X’s Dragon also included solid landings in their designs. But dropped in favour of the greater simplicity and reliability of water - for them.

Water is a good choice when your launch is next to, and out over, water. Then your abort landing is going to mostly be on water anyway. Landlocked launch facilities are going to need a land abort so may as as well land that way as well.

I wondered that, but I doubt it. Even if they did, they would just hold the tip of the capsule out of the water. Which isn’t going to help potentially injured astronauts inside. Given how near disaster Grissom’s flooding of the capsule was one would not want to count on it.

Yes, the Russian and Chinese spacecraft land on land. Their capsules fire a thruster right before touchdown to decrease the impact speed.

Bean got beaned?

“Pliant” isn’t the issue. Water has mass, and to get it out of your way so you can continue moving forward, you have to exert a force on it - which means it exerts a force back on you. If you want to get it out of your way quickly, then there’s a lot of force involved.

If you weigh 150 pounds and you are freefalling through the air at terminal velocity (~120 MPH), then the air is pushing upwards on you with 150 pounds of force. Water is about 800 times as dense as air, so when you hit the water at 120 MPH, you will suddenly experience 800 * 150 = 120,000 pounds of force. To be fair, that’s an oversimplification because you don’t have a broad flat surface that hits the water all at the same time, but you get the idea: there’s a huge amount of pressure directed at each square inch of your body that hits the water at high speed. People who jump from the Golden Gate Bridge tend to die from blunt force trauma - or if they drown instead, it’s because their bodies were so broken by the impact with the water that they couldn’t swim.

The same issue applies to the Apollo command module. Higher splashdown speed means higher splashdown force, and it’s something you can calculate.

All I meant by “pliant” is that hitting the water at 30 MPH is preferable to hitting the ground at the same speed…a speed at which many motorists hit a solid object every day and still survive, often without injury. The common wisdom that hitting the water at terminal velocity is the same as hitting the ground doesn’t apply in this case.

While I agree that hitting water isn’t the same as hitting solid ground, hitting water at high speed is definitely not a benign event; it’s just that hitting a solid object at high speed is even more violent.

FWIW, a car hitting a solid object at 30MPH sacrifices itself to protect its occupants. It’s a pretty violent event, and it takes seat belts, airbags, and a generous crumple zone to enable people to walk away from a crash like that (albeit probably with some bruising, possibly a broken rib and/or collar bone from the shoulder belt). Here’s a Volvo hitting a solid object at 35 MPH:

YouTube: Volvo 35-MPH crash test

For Apollo astronauts splashing down in the command module, the seawater itself functioned as a crumple zone/water brake. Certainly splashing down in water is better than slamming down on solid rock, but you still have to manage your splashdown velocity to keep it within acceptable limits - and my estimate is that a 30-MPH splashdown, while survivable for the astronauts, might cause problematic damage to the command module, e.g. cracks/tears in the hull that might allow water intrusion that compromises buoyancy.

Two publications that may be of interest: