About how the lunar environment makes everything tippier…
1) I’m sure the CLPS contractors know this and designed for it. My point is that the Moon does this to your hardware, so when things go wrong (as they do) then tipping happens more often than on Earth. /1
1) I’m sure the CLPS contractors know this and designed for it. My point is that the Moon does this to your hardware, so when things go wrong (as they do) then tipping happens more often than on Earth. /1
2/
2) There are different ways you can tip. For static stability, gravity makes no difference. You fall when you are so tilted that the center of gravity (cg) is outside of your footpad. I don’t know where the Nova-C has its cg, but crudely it could handle ~54 degrees tilt.
2) There are different ways you can tip. For static stability, gravity makes no difference. You fall when you are so tilted that the center of gravity (cg) is outside of your footpad. I don’t know where the Nova-C has its cg, but crudely it could handle ~54 degrees tilt.
3/
3) But for dynamic stability, gravity does make a difference. Imagine your vehicle is accidentally moving sideways at touchdown with velocity v. The energy of that motion is (1/2)m v^2 where m is the vehicle’s mass. The vehicle will fall over if that energy exceeds…
3) But for dynamic stability, gravity does make a difference. Imagine your vehicle is accidentally moving sideways at touchdown with velocity v. The energy of that motion is (1/2)m v^2 where m is the vehicle’s mass. The vehicle will fall over if that energy exceeds…
4/…the potential energy needed to lift the cg over its highest point as the vehicle rotates up and over the outboard footpad. So in this rough picture, if the cg is a 1 unit of height, it will be lifted to 1.268 units of height as the vehicle rotates up & over the footpad.
5/ So the change in height of the cg is deltaH = (1.268 - 1) = 0.268 units. The potential energy is (m g DeltaH). Tipping over occurs if this potential energy is less than the sideways kinetic energy. Solving for v, the tipping limit is
v>Sqrt(2 g DeltaH)
So now let’s reduce g.
v>Sqrt(2 g DeltaH)
So now let’s reduce g.
6/
Actually, let’s look at it this way:
Say it gets exposed to a sideways velocity v on the Moon that puts it barely at the edge of tipping. How wide would the footpads need to be on Earth (with 6x larger g) so that the same sideways would be at the edge of tipping?
Actually, let’s look at it this way:
Say it gets exposed to a sideways velocity v on the Moon that puts it barely at the edge of tipping. How wide would the footpads need to be on Earth (with 6x larger g) so that the same sideways would be at the edge of tipping?
7/ The DeltaH would be 1/6 as high for the same limit, so the factor of 6 and 1/6 cancel out. Solving the trigonometry, the footpads would have 0.3 units of width. Basically, straight down. If you built it with straight down legs, it would be pretty easy to tip, right?
8/ That’s how tippy it is on the Moon even with the wider legs. So on the Moon you have to design to keep the sideways velocities very low at touchdown, much lower than you would if landing the vehicle in Earth’s gravity.
9/ That doesn’t mean all kinds of tipping are the same as if the legs were straight down. If you land on a slope, the static stability doesn’t care about gravity so the wide legs make you stable on a slope the same as on Earth. This is only for the dynamic forces from unplanned
10/…motions at touchdown.
You can get unplanned motions several ways. (1) Navigation error. (2) Control failure. (3) Unlevel terrain causing the footpads to hit at different times, putting a torque on the vehicle.
IM was speculating that #3 happened. If you hit a rock and…
You can get unplanned motions several ways. (1) Navigation error. (2) Control failure. (3) Unlevel terrain causing the footpads to hit at different times, putting a torque on the vehicle.
IM was speculating that #3 happened. If you hit a rock and…
11/ it causes the vehicle to begin rotating slightly in the tilt direction, you rely on the width of the footpads to stop that rotation, but on the Moon it is like having footpads that are straight down, not spread out. So you have to keep the maximum possible rotation very low.
12/ You keep the rotation that would result from hitting a rock very low by having a descent rate at touchdown that is very low.
The whole mission is a tradeoff between risks though, and failures are usually from a combination of things happening together.
The whole mission is a tradeoff between risks though, and failures are usually from a combination of things happening together.
13/ You might have a small navigation error that gives you a residual sideways velocity at touchdown, which by itself is in limits, but made worse because blowing dust makes the navigation lasers less accurate at touchdown, which we can’t predict yet since we haven’t solved the…
14/…physics of blowing dust — so some guesswork went into designing the nav lasers and this is why we are doing the missions, to take the risks and solve the physics — and this may be combined with landing on a slight slope…
15/…that is amplified in a really unlucky way because a big rock ends up right under a footpad on the uphill side. So that footpad hits much sooner causing a torque that rotates the vehicle. The descent rate was designed to be low enough to handle that slope & rock by themselves
16/…but combined with the other errors you end up with more rotational/translational kinetic energy than the legs’ width was designed to handle in lunar gravity. You can be super conservative and design with even wider legs but it is a tradeoff of vehicle & mission requirements.
17/ I am sure the CLPS contractors know all this. My point is just that in lower gravity you will see some types of failures more often than you’ll see them on Earth, and tipping over is one of those things. This is why, IMO, two lunar landings in a row tipped over. /end
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