Terminal velocity

[stoani96]

Hello,

can someone please explain to me, why it is so important to not be faster than the terminal velocity during ascent?

(It seems to me important, because everywhere nearly everyone refers to it)

My thoughts:

If you ascent with terminal velocity(straight up of course), your TWR has to be 2.

If you ascent with half the terminal velocity, your TWR has to be 1.25. (half the speed, quarter the force)

If you ascent with the double terminal velocity, your TWR has to be 5. (double the speed, four times the force)

A "optimal" TWR of 2 for an ascent seems very randomly to me.... so why it is so important(mathematically explained, if possible)?

mfg

Edited January 8, 2014 by stoani96

[TechnicalK3rbal]

The terminal velocity is where the drag and the force of gravity are equal. If you go faster, the drag is more, but the gravity is less. So if your falling, you won't keep accelerating, you'll stop at the terminal velocity. If your ascending, this is the most efficient, because you have less drag, but you're still going fast enough to get out of the gravity.

[stoani96]

Is there an mathematically proof for that?

'Cause i think, there is not...

I know what the terminal velocity is.... i'm a budding aircraft engineer....

(and even if not, i could use google...)

[...]but you're still going fast enough to get out of the gravity.

Even if you are just 1m/s fast, you'll "get out of gravity"

It will take a while untill you are in space, but it would be possible

[Soda Popinski]

Hello,

If you ascent with terminal velocity(straight up of course), your TWR has to be 2.

If you ascent with half the terminal velocity, your TWR has to be 1.25. (half the speed, quarter the force)

If you ascent with the double terminal velocity, your TWR has to be 5. (double the speed, four times the force)

mfg

That is incorrect. If you have a TWR of 2, you accelerate at 9.81 m/s^2. If you have a TWR of 1, you do not accelerate. TWR of 1.5 accelerates you in between at 4.9 m/s^2. Acceleration rate doesn't equal velocity. Also check your math. Doubling 2 equals 4, not 5.

Terminal velocity, as stated above is the speed that the force of atmospheric drag equals the force of gravity - so when you drop a sky diver, they fall at terminal velocity (downward).

Since the atmosphere gets less dense the higher you go, there is less atmospheric drag, and terminal velocity increases with altitude. So the reason you want a TWR of about 2 is because this allows you to accelerate so your actual velocity matches closely with terminal velocity. Faster and you waste fuel fighting atmospheric drag. Slower, and you waste fuel on gravity "drag" (the worse example being a hover at TWR of 1).

[tavert]

It's called the "Goddard problem." Gravity losses per unit altitude are inversely proportional to vertical speed. Drag losses are proportional to speed squared. For vertical ascent through a constant-density atmosphere, the optimal tradeoff between the two is at terminal velocity. For exponential density vs altitude, and neglecting surface rotation and the variation of gravity with altitude, you can get a variational calculus derivation that keeping up with terminal velocity as it varies with altitude is optimal in these conditions too.

[stoani96]

That is incorrect. If you have a TWR of 2, you accelerate at 9.81 m/s^2. If you have a TWR of 1, you do not accelerate. TWR of 1.5 accelerates you in between at 4.9 m/s^2. Acceleration rate doesn't equal velocity. Also check your math. Doubling 2 equals 4, not 5.

Are you kidding me!?!?!?!?!?

Did ever ever saw a school from the inside? (its not meant badly!)

(If you are talking about vacuum operations, what i do not belive, i want to a excuse right here!)

A simple equation:

Thrust = Weight + Dragforce

The upgoing force equals the downgoing forces, if there is no acceleration, what we will assume. (Because if der is no acceleration, there is no change in speed, we maintain this speed)

It seems we agree in the definition of terminal velocity. It is the speed at wich the force caused by the air(the so called drag) is equal to the weight. dragforce=weight

if we put this in the formula from above we get:

Thrust = Weight + Weight = 2*Weight

As we all know: TWR is the Thrust-Weight-Ratio:

Thrust/Weight=TWR

with the formule form above:

2*Weight/Weight=TWR

-> TWR=2

i hope thats clear now!

Next one:

2^2=4 thats right, but to maintain a speed that is 2 times the terminal speed, you will need a TWR of 5... why?

lets see:

Thrust=Weight+Drag

as we all know(if not, please use google) if we double the speed, we will have four times the drag. (v^2)

So Drag=4*Weight

Thrust=Weight+4*Wheigt=5*Weight

TWR=5

To make it clear!

I'm from Austria, so my english is not perfect ^^, i'm 18 years old and an budding aircraft engineer, so I've already got some knowledge about aerodynamics!

[stoani96]

It's called the "Goddard problem." Gravity losses per unit altitude are inversely proportional to vertical speed. Drag losses are proportional to speed squared. For vertical ascent through a constant-density atmosphere, the optimal tradeoff between the two is at terminal velocity. For exponential density vs altitude, and neglecting surface rotation and the variation of gravity with altitude, you can get a variational calculus derivation that keeping up with terminal velocity as it varies with altitude is optimal in these conditions too.

THANKS!

It seems you are the only one, who really read my question...

Its so clear.... How have i been so dump?

2 is not randomly, its the intersection of the two functions!

Thanks a lot!

[Alistone]

Hello,

can someone please explain to me, why it is so important to not be faster than the terminal velocity during ascent?

(It seems to me important, because everywhere nearly everyone refers to it)

My thoughts:

If you ascent with terminal velocity(straight up of course), your TWR has to be 2.

If you ascent with half the terminal velocity, your TWR has to be 1.25. (half the speed, quarter the force)

If you ascent with the double terminal velocity, your TWR has to be 5. (double the speed, four times the force)

A "optimal" TWR of 2 for an ascent seems very randomly to me.... so why it is so important(mathematically explained, if possible)?

mfg

It is just representing the point that the force of gravity is balanced by the force of wind resistance and thus a falling object stops going faster.

As the point where the two forces are equal it is the optimal balance between gravity losses and air resistance losses.

It is NOT the same as a TWR which has to be above 1, but below 10,000 meters it seems can easily be less than 2 to maintain terminal velocity during ascent.

[TimMartland]

I think its kinda the point where, if you go faster, your extra speed will be wasted as the atmosphere at that point will slow you down. Thats why it gets bigger the higher on Kerbin you go, and why there isn't any in space. I don't know the scientific explanation tho.

[stoani96]

PLEASE READ MY OWN ANSWERS ON THIS TOPIC!

TWR has to be 2 to maintain terminal velocity, otherwise its not the terminal velocity

[tavert]

TWR has to be 2 to maintain terminal velocity, otherwise its not the terminal velocity

Only if the atmospheric density is constant, then a constant TWR of 2 will lead your velocity to asymptotically approach terminal velocity. In reality atmospheric density decreases as you ascend. To maintain terminal velocity you need a TWR slightly higher than 2 to provide the net acceleration to keep up with terminal velocity as it increases. Also keep in mind that TWR increases as you burn fuel.

[stoani96]

Only if the atmospheric density is constant, then a constant TWR of 2 will lead your velocity to asymptotically approach terminal velocity. In reality atmospheric density decreases as you ascend. To maintain terminal velocity you need a TWR slightly higher than 2 to provide the net acceleration to keep up with terminal velocity as it increases. Also keep in mind that TWR increases as you burn fuel.

Thats right!

Its just roughly and assuming that we look at a very short time periode (everything is constant), just to show how it works

Because of the atmospheric curve, i think the twr also has to raise a bit during ascent, cause density is not decreasing lineary.

But you can never do it really perfectly, that's perfectly impossible

[Taki117]

Hello,

can someone please explain to me, why it is so important to not be faster than the terminal velocity during ascent?

(It seems to me important, because everywhere nearly everyone refers to it)

My thoughts:

If you ascent with terminal velocity(straight up of course), your TWR has to be 2.

If you ascent with half the terminal velocity, your TWR has to be 1.25. (half the speed, quarter the force)

If you ascent with the double terminal velocity, your TWR has to be 5. (double the speed, four times the force)

A "optimal" TWR of 2 for an ascent seems very randomly to me.... so why it is so important(mathematically explained, if possible)?

mfg

Terminal Velocity is the point at which your air resistance is maximum. In the case of Free fall it's the point at which your drag due to air resistance equals your acceleration due to gravity and as such you cannot fall faster. Now Let's apply this to something that is accelerating upwards (A rocket). As you increase your velocity you are compressing the air in front of you (Hence why Most rockets are pointy, to reduce this compression) This is known as drag. Now, why do we stay at or below terminal velocity? (In an ideal situation we would always stay at exactly terminal velocity) We do this because Terminal Velocity or an accelerating body is the point at which Thrust losses due to gravity and thrust losses due to drag are equal. IF you go any faster you are wasting fuel to fight air resistance and drag. Any slower and you are wasting fuel fighting gravity.

[stoani96]

Terminal Velocity is the point at which your air resistance is maximum. In the case of Free fall it's the point at which your drag due to air resistance equals your acceleration due to gravity and as such you cannot fall faster. Now Let's apply this to something that is accelerating upwards (A rocket). As you increase your velocity you are compressing the air in front of you (Hence why Most rockets are pointy, to reduce this compression) This is known as drag. Now, why do we stay at or below terminal velocity? (In an ideal situation we would always stay at exactly terminal velocity) We do this because Terminal Velocity or an accelerating body is the point at which Thrust losses due to gravity and thrust losses due to drag are equal. IF you go any faster you are wasting fuel to fight air resistance and drag. Any slower and you are wasting fuel fighting gravity.

Somethings wrong with (the most) guys in this community.... not meant bad!

I ask for an explaination, why it is so! Not what the terminal velocity or something else is!!!! (i mean, its even googable!)

If someone wants a complicated answer give him a complicated one, especially if he mentions that he has knowledge in aerodynamics!!

If you do not know exactly why this is so:

a) mention that you have no idea

do not put your two cents in!(its kinda google translator, in Austria we say: "seinen Senf dazu geben", if anyone knows that)

So again: A very special thank to tavert, who actually read my question and answed it and explained it and seems to have a clue (sry, i meant, has a clue!)

Edited January 8, 2014 by stoani96

[Soda Popinski]

PLEASE READ MY OWN ANSWERS ON THIS TOPIC!

TWR has to be 2 to maintain terminal velocity, otherwise its not the terminal velocity

No, it doesn't. It's a good rule of thumb on Kerbin, but a TWR of 2 doesn't equal terminal velocity.

Let's say you are on Mun, with a surface gravity of 1.63 m/s^2. Let's say your spacecraft is 1t, meaning 1.63 kN of weight. If you thrust with 2x of that, or 3.26 kN of force upward. Are you moving at terminal velocity?

No, because there is no atmosphere, and hence no atmospheric drag, therefore terminal velocity is infinite. You still have a TWR of 2, and will accelerate at 1.63 m/s^2, but you are nowhere near terminal velocity.

[Alistone]

Interesting point that at a t/w ratio of 2 maintains terminal velocity.

I said that a t/w ratio of less than 2 has worked fine for me in the past - that was my T/W ratio at the beginning of the stage, but after burning fuel I realize now I nearly always end up with a t/w ratio above 2 before I reached the end of the stage. Considering between 20%(fist asparagus stage) to 50% (last asparagus before the core) of my vehicle mass would be burned that would change the t/w ratio to be abover the optimal 2+ a bit you quote.

The first radial asparagus stage with a t/w ratio of 1.8 at the beginning of a stage but after losing 20% of the stage mass to fuel burning it ends with a t/w ratio of 2.25

The second asparagus stage with a t/w ratio of 1.8 at the begining of the stage burns 35% of the stage mass and ends with a t/w ratio of 2.75

The last radial asparagus stage burns over 50% of the ship mass in fuel changing a T/W ratio of 1.8 to 3.6

I was only looking at the beginning of the stage t/w ratio. Now I see plainly that 2 (plus a tiny bit) is the place to be on average. I just tend to start below that so I stay close to it throughout. Always a good day when I can learn something new.

[stoani96]

No, it doesn't. It's a good rule of thumb on Kerbin, but a TWR of 2 doesn't equal terminal velocity.

Let's say you are on Mun, with a surface gravity of 1.63 m/s^2. Let's say your spacecraft is 1t, meaning 1.63 kN of weight. If you thrust with 2x of that, or 3.26 kN of force upward. Are you moving at terminal velocity?

No, because there is no atmosphere, and hence no atmospheric drag, therefore terminal velocity is infinite. You still have a TWR of 2, and will accelerate at 1.63 m/s^2, but you are nowhere near terminal velocity.

sry but thats total bull excrement (<- I hope this is okay ^^)

why?

Cause, like you say, the terminal velocity does not exist! (on e.g. mun)

Therefore this thumbrule is only okay on bodies with atmosphere!

But thats more than logic ;D

Edited January 8, 2014 by stoani96
No profanity

[Ravenchant]

So, TWR rule-of-thumb for all bodies:

-if it has an atmosphere: ideally, 2 or slightly above at all times

-on non-atmospheric bodies: as much as your craft can take without disintegrating

[Aphox]

I think the author of the thread has gotten what they came for.

Closed.