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# Drag Co efficent watch

1. Hello, just a quick one.

I’m doing a project at the moment. About a space shuttle entering the earths atmosphere.

The space shuttle starts off with v = 0 and falls in free fall for 30km. I’m using f =Ma. Up until is enters the earths atmosphere and the has a drag Co efficient.

The thing is that the final v I get using suvat, when I enter the v into the drag bv squared equation i get some insane results. It flys back outside the atmosphere.

How do I combine f = Ma and f - bv2 = Ma for free fall and air resistance.
2. I think the problem you are having is because the v in bv2 is constantly decreasing as the speed decreases and will do so until the shuttle reaches terminal velocity.

At terminal velocity, there is no unbalanced force on the shuttle (and therefore the accerelation . or deceleration in this case) is zero. In other words, the force due to gravity is exactly equal to the drag force.

Does that help you? Are you trying to find the final velocity as it approaches earth?
3. Maybe. Probably my fault for not explaining too well

The shuttle is 130 km above the Earth.

Initially the shuttle free falls for 30km. At 9.81 ms. So I use suvat and get about 760 ms for v at 30km

The air resistance effects the speed. The bv2 equation. The shuttle weigh 1000 kg so when I input v as the speed I get a

Mg - bv2 = Ma
1000x9.81 - bx760’square= Ma

I’m obviously wrong.

Is there an equation in between?
4. (Original post by Cristianvieri)
Maybe. Probably my fault for not explaining too well

The shuttle is 130 km above the Earth.

Initially the shuttle free falls for 30km. At 9.81 ms. So I use suvat and get about 760 ms for v at 30km

The air resistance effects the speed. The bv2 equation. The shuttle weigh 1000 kg so when I input v as the speed I get a

Mg - bv2 = Ma
1000x9.81 - bx760’square= Ma

I’m obviously wrong.

Is there an equation in between?
So air resistance starts at 100km to the gound
5. (Original post by Cristianvieri)
The air resistance effects the speed. The bv2 equation. The shuttle weigh 1000 kg so when I input v as the speed I get a

Mg - bv2 = Ma
1000x9.81 - bx760’square= Ma

I’m obviously wrong.

Is there an equation in between?
I still think that's the issue . that equation is only correct for a fraction of a second because the instant the drag force kicks in, the 760 m/s starts to decrease. And then mathematically that becomes a bit complicated to deal with.

What are you taking as b? Or are you trying to calculate that?

Sorry, it's late and I'm done, I'll have another look tomorrow. In the meantime if you can explain exactly what it is you're trying to calculate that would help.
6. I know b. I can find it. Thanks for your help btw,

So drag is going to be 760x760 I think it’s like 0.35 ish b.

So 1000x981 - bv2 = 1000a

So a is -192 ms approx until it stablises?

I’m tired. I actually woke up today thinking about this stuff. In my haze when I was half a awake.
7. If I understand correctly what you're doing, a will be calculated as you say but only at the instant at which it enters the atmosphere.

Immediately the 760 will start to decrease which will change your a as well.

Your a will continue to change until it reaches 0 and then you have terminal velocity.

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