Terminal velocity equation

[kragon]

Now that we have 0.24 and there money to worry about (well there's money anyway) I'm trying to design a returnable upper stage.in order to save weight and money I'm using as few parachutes as possible,which generally means the craft hits the ground too fast for the engine to handle, so to cushion the landing I've been using sepertrons because ,even when there full ,they still weigh less than half of a radial parachute and it makes landing a bit more interesting.

however they are rather annoying to set up,either launching the craft back into the air where the parachutes auto-cut and it crash back to kerbin,or it doesn't slow it enough and it crushes the engine (I don't like using the revert options as it makes the new money mechanic too easy and explosions are fun)

now my question is: does anybody know what is the equation to calculate the terminal velocity of a craft while factoring in a constant thrust?

assuming surface gravity and air pressure as well as constant weight

[Clockwork_werewolf]

I can't answer the terminal velocity part but there are other things.

1: Are you using any landing legs?

2: Whats the mass of the lander?

3: How many parachutes are you using?

4: Why not add wings and a jet engine to get to back to KSP for the full 100% refund? (unless your aim is perfect).

5: Have you tried lowering the fuel in the sepotrons so their weight is less but they also do more of a punch than a long burn?

6: Why not add a few more parachute so that the window of error is bigger?

I'm interested in this idea though, I tried this a bit in 0.23 but there was no real purpose to it.

[pellinor]

If there is an engine to crush, why not keep a little fuel and use the engine you already have? Since SRBs have about the worst ISP in the game, you'll even save weight this way.

[Yasmy]

Given your assumption of constant mass (i.e., the sepratron fuel mass is tiny),

use the terminal velocity equation in http://wiki.kerbalspaceprogram.com/wiki/Atmosphere,

but replace GM/r^2 with (GM/r^2 - TMR).

v = sqrt( 250 kg/m^2 * (GM/r^2 - TMR) / (rho * d) )

TMR = number of sepratrons * thrust of a single sepratron / mass of return vehicle

(i.e., TMR = TWR * g0 = 9.82 m/s^2 * TWR)

Edited July 27, 2014 by Yasmy

[KerikBalm]

note you can tweak the thrust of the sepratron in he VAB, jut not in flight, if it gives too much thrust, lower it in the VAB, this also gives you a longer "cushion" time.

But for very low velocities, the drag is very small, there isn't much difference in drag between 7 m/s down or 3 m/s up, and I think it will be quite hard to do without a throttleable engine

[Torham234]

If there is an engine to crush, why not keep a little fuel and use the engine you already have? Since SRBs have about the worst ISP in the game, you'll even save weight this way.

I usually do it this way as well. Decoupling the last stage engines before reentry seems like a waste of money for me, so I just keep the last stage in one piece. This makes it usually too heavy to just land on parachutes, so I keep a tiny bit of fuel in the tanks. Immediately before touch down ( 10 - 15 m above ground) I fire up the engine a slow down enough to safely land. landing legs are nice, but they weigh quite a bit, so that would defeat the OP aim of minimal weight reentry vehicle.

[Clockwork_werewolf]

I've been playing around with land things hard using different combinations of Sepratron, parachutes and landing legs.

I was using a 13 ton lander with a fuel tank (6m/s impact tolerance) on the bottom do make it harder as most pods have a high impact tolerance.

Two Sepratrons (minimum to have central thrust) reduced the speed by 2m/s at 12-14 m/s. The mass for these was 0.0725 per sep that's 0.145 in total.

One small parachute reduced the speed after opening to roughly 22-23 m/s. The mass for this was 0.1.

One large or two radial parachutes reduced the speed after opening to roughly 13-14 m/s. The mass for these was 0.3.

Three radial parachutes reduced the speed after opening to roughly 9.4-9.6 m/s. The mass for these was 0.45.

Four radial parachutes reduced the speed after opening to roughly 8.3-8.5 m/s. The mass for these was 0.6.

Three medium landing legs would semi break on impact under about 16m/s. They would be FULLY recoverable for all funds but no longer compress or extend. Their mass was 0.05 so 0.15 in total.

Adding a whole bunch of wings made it possible to sometimes land the craft on the runway for a full 100% recovery. 2 delta wings, 2 small control surfaces, 4 AV-R8 wingless and 2 swept wings were used for a mass of 0.34. 3 Landing gear were used but they are mass-less in flight. The craft was quite hard to fly and not all tests were landed safely.

Halving the fuel in the Sepratrons allowed me to reduce their mass to 0.0425 per sep. This amount of fuel meant it was difficult to time their firing correctly to not cut out before landing. At any speeds above 14 m/s it was very difficult to time the firings right even with full fuel.

In conclusion:

The best 100% recoverable lander used one large parachute or two radials with 3 medium landing legs. This was 0.45 tons total landing gear for 13.12 tons of lander, meaning landing gear was 3.4% of the mass of the lander. Somewhere between 22 and 43 tons this setup no longer guarantied a safe landing.

The lightest lander was using wings but the craft was not very easy to control of land. It did however let me land on the runway (sometimes) for a full refund.

With an automatic Sepratron firing mechanism and 50-25% fuel in each it might be possible to build a lander with a reduced mass than this. Due to human error I couldn't get this to be mass effective in any test even when repeated multiple times. The Sepratron uses 2.44 fuel a second. If an automated device could be designed to fire at one second from the ground then each Sepratron could be reduced to 2.4 fuel from 8 and its mass reduced to 0.0305. At this mass 4 could be used for less mass than a radial parachute (0.0305 x 4 = 0.122). Correct use of low number of parachutes with a heavy lander and Sepratons for the last second before landing could result in a low mass but is very difficult in reality.

Edited July 28, 2014 by Clockwork_werewolf

[kragon]

1:I'm not using landing legs there generally just excess weight and they aren't that much stronger than an engine

2:I've normally got a whole family of them so normally anything from 5 tons to 30 tons when empty (the ones worth recovering at least)

3: usually 2 radials or a mk16 just enough to give it a constant decent speed

4:I can normally land and lose about 1-2% of the value and wings generally look correct and fly like a brick, or look silly and fly well. I also tend to ignore the plane parts in the tech tree till I have science to burn.

5,6: I'm only using the sepertron to negate some of the landers mass so that it's decent speed with the parachutes is lower

so all that lowering the fuel would do is reduce the time the lander is slow enough to land (also the change in twr from a full sepertron to an empty one is fairly insignificant for a larger craft)

parachutes are really expensive in comparison to sepertrons but without a formula I don't know at point parachute become more effective

the problem I've found with using the main engine is that it relies on me remembering to save a bit of fuel.there also a lot harder to judge the correct thrust where as sepertrons can be preconfigured and only require staging.

Edited July 28, 2014 by kragon

[Laie]

1:I'm not using landing legs there generally just excess weight and they aren't that much stronger than an engine

Legs have their worth when you have NO thrust. It takes only a few parachutes to bring a craft down to 12m/s (safe for legs) but it takes many, many more chutes to bring it down to the 6-7m/s that most other parts can withstand. In that case, 300kg worth of legs can save you 5 tons of parachutes. A Clampotron Senior at the bottom is even better than legs, by the way.

the problem I've found with using the main engine is that it relies on me remembering to save a bit of fuel. there also a lot harder to judge the correct thrust where as sepertrons can be preconfigured and only require staging.

Well, I always have some fuel left. If you found a reliable way of bringing just the right amount, I'd really like to know how you do it -- I can't. Given the choice of having either too much or too little fuel during a mission, I like to err on the side of caution. This also means that i have some fuel left during/after re-entry. Nearly any amount of fuel is excessive for the task at hand.

In my case it's just the opposite: I'd never trust my ability to ignite the sepratrons at just the right time. As to judging the correct thrust, well, that's what the throttle is there for. I start thrusting perhaps five seconds before touchdown (slowly count to five, that's a lot of time for throttling up and down and finding the right setting).

[kragon]

v = sqrt( 250 kg/m^2 * (GM/r^2 - TMR) / (rho * d) )

TMR = number of sepratrons * thrust of a single sepratron / mass of return vehicle

Thank you yasmy

collapsing the variables gives

Vt=Sqrt((2011·(1-twr)·M)/(Mc·0.2 +Mp·500))

assuming kerbin sea level

M being total mass

Mc being mass without parachutes

Mp being mass of parachutes

twr being the twr of the sepertrons

[Clockwork_werewolf]

1:I'm not using landing legs there generally just excess weight and they aren't that much stronger than an engine

See above post, 3 medium landing legs can take about 22 tons landing at 14 m/s. Only 4 engines (rapier, toroidal, LFB KR-1x2 and S3 KS-25x4 Engine Cluster) can beat this for impact speed.

The 3 legs are equal in mass to just ONE radial parachute. Laie is very right about parachute speeds. 14m/s is easy, 7m/s is very hard.

ONLY partly filled Sepratrons can beat a parachute for mass to thrust/drag. Unless the pod is so tiny that the mass of parachutes needed is so tiny its not worth talking about.

An automated Sepratron firer would work though. Unless you have that you can't beat parachutes for mass. I tend to feel that the cost of the extra mass in fuel/engines/tanks greatly outweighs the savings in Sepratrons/parachutes.