Understanding Delta-V

[Jarin]

So, I typically use Engineer to calculate my lift vehicles' needed fuel, but I have a question about how it works. Specifically, how TWR and Delta-V interact. Obviously, a ship with TWR of less than 1 can't get off the ground, and isn't going anywhere, regardless of how much Delta-V it has. But it seems like there should be a curve above 1 where Delta-V is less useful than the flat numbers suggest.

For example, it takes somewhere around 4500 delta-v to get into a stable Kerbin orbit, right? Now, say I have two ships with this delta-v value. One has a TWR of 2 (easy orbital ascent, right?) and the other has a TWR of 1.01. Now the latter is going to burn most of its fuel just trying to accelerate at all, right? Where's the changeover between "burns all fuel and hardly goes anywhere" and "reaches orbit fine"? It seems like there should be some sort of effectiveness curve, but Engineer doesn't seem to alter the Delta-V estimates based on thrust at all. How do I calculate this effect? Or am I completely misunderstanding how Delta-V works?

Edit: I understand that TWR has no effect on ships already in space. This is a question strictly about launching from KSC (and related, launching from other orbital bodies).

[RadHazard]

More TWR means less drag losses when you launch, but it's partially dependent on your launch profile. I believe MechJeb has an in-flight readout that tells you how much dV you've lost from drag since you've launched, but I don't know if Engineer has the same thing.

I'm not sure if there's an easy way to calculate this beforehand.

[Taki117]

MechJeb also has the ability to limit your craft to terminal velocity as you launch, which limits losses due both to gravity and drag.

[MrChumley]

From KSC The faster ship will be more efficient because it spends less time in the atmosphere... right up until it tries to go faster than it's terminal velocity then efficiency starts degrading again due to drag.

TWR effects how fast you are able to change velocity (in space or atmosphere)...

[Godot]

Yes, the ship with the TWR of 2.0 will lose less dV due to drag than the one with 1.01, as it spends les time in lower altitudes, where drag is higher.

But with a TWR of 2.0 it is also easy to get over the terminal velocity of the altitude you are in, therefore you should always look at the Terminal velocity (which can be shown in the Kerbal engineer flight panel) and lower your thrust accordingly if you get over it (as a speed higher than TV means rapidly rising drag).

Also, you have the option, when building a ship with Kerbal Engineer integration, to get shown the dV that is modified by the atmosphere (at sea level) of your chosen body of reference (by clicking on "Atmosphere") ... that gives you a few indicators of the loss (although, as the full drag only applies in the lower altitudes, you sould only take this value inbto acount for the first few stages (or even just the first one) of your rocket.

Also, as soon as yur are in orbit, TWR doesn´t ply such an important role anymore, as you usually have enough time for maneuvers in space (and therefore a lower TWR -> longer burn times doesn´t affect you this negatrively anymore)

[Frederf]

TWR has nothing to do with dV directly. Indirectly high TWR engines tend to be lighter and so the propellant mass fraction improves all other construction equal. dV is efficiency times mass fraction (logarithmically, that is). TWR doesn't enter into it.

deltaV requirement for a maneuver will change based on TWR as non-optimal setup will result in increased dV requirement. With 1.1 TWR LKO could take many thousands of m/s of dV more than 4500.

The optimal can be thought of as minimizing total loss, drag and gravity, which happens to be when they equal each other. This happens to be freefall terminal velocity (but up instead of down) which requires ~2g acceleration to keep at.

[EtherDragon]

Hi Jarin,

You make an astute observation that a rocket with very little TtW ratio is going to use more fuel getting into orbit - and it's effective Delta-V (dV) is going to be low. However, dV isn't calculated taking into account things like atmospheric drag and gravity. It's just the pure outcome of a single equation called the "Rocket Equation."

Source: Wikipedia - http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation

This equation calculates the total dV (given ideal conditions) that the rocket is theoretically capable of.

Basically, to know the (ideal) dV of the rocket you have to take into account several factors:

The Isp (in the equation it's Ve) is where the rocket engine comes into play. The other bits are the ratio of empty mass to full mass.

Notice, that the equation doesn't take any other factors into consideration. It's more accurate to say that the Rocket Equation can predict your rocket's dV in a vacuum.

Heh, now I need to make a Korbital Mechanics lab on the Rocket Equation. =p

[Superfluous J]

There are a lot of factors. I boil them all down to "Get to terminal velocity quickly and then stay there, but try not to throttle down your engines too much (if at all) to do so." This simple rule requires you to balance TWR, Delta V, amount of fuel in each stage, how efficient your engines are, and all that. It can be quite a juggling act to get that nice buildup of speed that doesn't spend too much time below - say - 90% of terminal velocity but also never goes over 100% of terminal velocity, and also doesn't require throttling down.

Why don't you want to throttle down? When you put bigger engines on your ship you sacrifice efficiency for power. If you throttle down you're losing power but keeping that same poor efficiency.

[capi3101]

Folks have been playing around with finding optimal balances between delta-V and TWR for a while now. Largely depends on how you've set your rocket up, but as a rule you want to keep your TWR during launch somewhere in the 1.6-2.2 range; that best follows the terminal velocity curve. It's also one of the reasons why folks will tell you to use asparagus staging - properly set up, you stay in that optimal TWR range without having to adjust the throttle. It basically winds up having the same affect as throttling back (i.e. when you stage, you're losing some thrust) but with the benefit of chucking off mass that's no longer necessary at the same time. Ultimate benefit is a very efficient rocket that will allow you a substantially larger payload fraction than other forms of staging.

Minimum acceptable TWR I find for launch is about 1.2; that's what I aim for when I'm designing SSTO rockets (usually for very light payloads only). Below that and the gravity losses are horrendous.

And BTW, TWR still is important once you're in space, just not as important as it was/is during launch and landing. Delta-V is critical throughout an entire mission.

[maccollo]

Move aside as I will perform math, even tho I suck at it and I might well be wrong and don't know what the hell I'm doing. If I'm wrong here please correct me....

Anyway...

During launch you will loose deltaV to drag and gravity. Gravity losses are a function of time, to the lower your TWR the higher your gravity losses will be.

Drag losses are a function of your velocity squared times the amount of time you spend in the atmosphere plus some other variables.

y=x/(x*x)+x

This oversimplified equation shows roughly the relationship between gravity losses and drag losses as a function of your velocity where X represents terminal velocity and Y relative gravity+drag losses.

As you can see, as the velocity approaches 0 gravity losses approach infinity. This is why you really really don't want to linger with a low TWR at launch.

Drag losses increase linearly, because while the drag deceleration increases by the square of the velocity, your increased speed means you spend less time in the atmosphere. So, say you go 4 times faster, the drag deceleration per unit of time becomes 16 times higher, but then you divide that by 4 again since you only spend 0.25 times as long in the atmosphere.

Now I thought this up this with the assumption that terminal velocity is the most efficient speed, and thus a TWR of 2.0 is the most efficient.

However more TWR for any given mass means less deltaV, so I'd wager the ideal TWR is a bit lower.

Edited November 3, 2013 by maccollo

[Kasuha]

TWR is always relative to local gravity. TWR 1 means you're just able to hover, i.e. you spend all your dv on fighting gravity.

If your TWR is higher, "1" of it always goes to fight gravity. So if your TWR is 2, half your dv is spent to fight gravity and half is used to ascend. If your TWR is 3, 33% is lost to fight gravity.

As you're getting to orbit, you are compensating gravitational pull by centripetal force generated by your horizontal speed. Thanks to that, your effective weight decreases and your effective TWR is growing.

[EtherDragon]

Move aside as I will perform math, even tho I suck at it and I might well be wrong and don't know what the hell I'm doing. If I'm wrong here please correct me....

Anyway...

During launch you will loose deltaV to drag and gravity. Gravity losses are a function of time, to the lower your TWR the lower your gravity losses will be.

Drag losses are a function of your velocity squared times the amount of time you spend in the atmosphere plus some other variables.

y=x/(x2*x)+x

This oversimplified equation shows roughly the relationship between gravity losses and drag losses as a function of your velocity where X represents terminal velocity and Y relative gravity+drag losses.

As you can see, as the velocity approaches 0 gravity losses approach infinity. This is why you really really don't want to linger with a low TWR at launch.

Drag losses increase linearly, because while the drag deceleration increases by the square of the velocity, your increased speed means you spend less time in the atmosphere. So, say you go 4 times faster, the drag deceleration per unit of time becomes 16 times higher, but then you divide that by 4 again since you only spend 0.25 times as long in the atmosphere.

Now I thought this up this with the assumption that terminal velocity is the most efficient speed, and thus a TWR of 2.0 is the most efficient.

However more TWR for any given mass means less deltaV, so I'd wager the ideal TWR is a bit lower.

One tiny correction, when you say "Gravity losses are a function of time, to the lower your TWR the lower your gravity losses will be." I think you meant "Gravity losses are a function of time, to the lower your TWR the higher your gravity losses will be."

You have a good simplified explanation, Maccollo. Like I say in my Ascent Profiles video, "Achieving orbit is the balance between two competing goals: Reaching orbit quickly to save propellant with respect to gravity, and avoiding high atmospheric speeds to save propellant with respect to drag."

[Nao]

I would add one more important element that is ofter overlooked in this kinds of discussions. The engine mass. High TWR means high engine mass. During burns fuel is used to accelerate itself, payload and engines. If we increase TWR, we allocate more energy from fuel to accelerate the engines themselves.

This is why while mathematically the best speed to ascent is at terminal velocity (TWR~ 2) the least fuel will be spent by using ship with TWR~ 1.8, and the smallest liftoff mass will be achieved at TWR~1.6. The deltaV required to achieve orbit will increase but with less engine mass the fuel mass fraction will increase, giving the ship more deltaV than it looses to the gravity drag using lower TWR.

[maccollo]

One tiny correction, when you say "Gravity losses are a function of time, to the lower your TWR the lower your gravity losses will be." I think you meant "Gravity losses are a function of time, to the lower your TWR the higher your gravity losses will be."

Fixed. Also noticed I wrote the equation wrong. There was a 2 in there that shouldn't have been there.

http://tinyurl.com/odah4n9

[Jarin]

I... my brain hurts. X_X

So, let's just go for rule-of-thumb here. Aim for 1.2-2 TWR, and expect to burn 4500~ish dV reaching orbit?

[Superfluous J]

I... my brain hurts. X_X

So, let's just go for rule-of-thumb here. Aim for 1.2-2 TWR, and expect to burn 4500~ish dV reaching orbit?

Expect to burn 5000 and be happy when you have some left over. But other than that yeah.

[Nao]

I... my brain hurts. X_X

So, let's just go for rule-of-thumb here. Aim for 1.2-2 TWR, and expect to burn 4500~ish dV reaching orbit?

Yes and no, if your TWR at its lowest point during flight (not counting the last 500m/s when you are almost in orbit) is above 1,7 then you can expect 4500m/s dV to orbit.

1,5 TWR rocket can expect ~4900m/s dV, and 1,2 TWR (would be ok for SSTO, and pretty bad for staged rocket) and probably burns around 5300+m/s dV.

edit: ninjaed

[Silicon014]

Typically, what I use is a launch stage that has a 1.8 TWR or more, as it needs to be powerful for the first section of the atmosphere. Honestly, you want to have just enough thrust to be able to reach terminal velocity throughout all stages of your liftoff: this speed is roughly 150 m/s at 4000 meters, 215 at 8000 meters, and 275 passing 11000 meters. If you're pushing your craft faster than terminal velocity, you're just fighting unnecessarily against the atmosphere. From then on, you can have as much thrust as you want for the final push into space. Also, you may want to stick with the lowest TWR and highest Isp possible in space for efficiencies' sake; however, if you wish to trade efficiency for speed (as in a higher TWR and subsequently higher thrust), you can.

[AmpsterMan]

I... my brain hurts. X_X

So, let's just go for rule-of-thumb here. Aim for 1.2-2 TWR, and expect to burn 4500~ish dV reaching orbit?

I look at it this way: By doing a arguably good ascent with a TWR of 1.8, I expect to get to orbit with 4600 Dv of Fuel. Doing A good ascent with lower TWR, say 1.2 I expect to use about 4800-4900 dv.

As a personal rule, I like to go with higher TWR's for a very simple reason. Fuel doesn't cost me anything in this game, but getting to orbit costs me something far more valuable. My time. The difference between a low TWR lifter and High TWR lifter in terms of time can be quite staggering; about two to three times faster.

[Sirine]

Agree with @AmpsterMan, Times count. (Real world time)

I normally don't care about Delta-V, I just make big rocket (Muooore boosters), and let it take-off, as long as it climb up fast. Its good.

Thats the Kerbal way. (Muooore boosters)

[Sirine]

But I do refer to something... http://wiki.kerbalspaceprogram.com/wiki/Kerbin#Atmosphere

Altitude (m) Velocity (m/s)

75 100.9

1000 110.5

2000 121.9

3000 134.5

4000 148.4

5000 163.7

6000 180.6

7000 199.3

8000 219.9

9000 242.6

10000 267.7

12500 342.4

15000 437.8

20000 716

32000 2332

3 lines. I gravity turn when matching the speed (m/s) / and altitude above. Mostly I turn at 6k, cause my rocket will be about 180m/s at that altitude.

[Kasuha]

My most effective gravity turns are when I am at 45° no sooner than at 25000 meters. Whenever I turn sooner I end up burning off-prograde to not fall again.

And I have no idea how much dv or TWR my rocket has. I do it the Kerbal way too. Trial and error.

[capi3101]

Yes and no, if your TWR at its lowest point during flight (not counting the last 500m/s when you are almost in orbit) is above 1,7 then you can expect 4500m/s dV to orbit.

1,5 TWR rocket can expect ~4900m/s dV, and 1,2 TWR (would be ok for SSTO, and pretty bad for staged rocket) and probably burns around 5300+m/s dV.

edit: ninjaed

Actually, the SSTO rocket would still do 4500 m/s of delta-V for orbit, but you have to be a little more careful about how you pilot it. That's from observation/experience.

The booster's TWR increases as you go, typically reaching the magic 1.6-1.8 range about the time you reach the tropopause. Turn at 45 degrees along 090 and hold that course until the apoapsis is 30-35 seconds ahead, then start following the navball. Meanwhile the TWR will continue to rise as the atmo gets less dense and the rocket gets lighter; eventually it'll get above the 2.2 mark, which is where folks say you start losing delta-V to atmospheric drag. That's when you throttle it back into that 2.0-2.2 range. And you keep doing that. Once the apoapsis is greater than 45 seconds ahead, you can start burning horizontally (090 along the horizon). Continue to monitor the throttle - actually, the best way to keep checking this is the gee meter; you want it near the top of the green zone without climbing out of there. Kill the burn when the apopasis is about 10k above where you want it (you'll probably still be in significant atmo when this happens; this compensates for the drag as you coast), then burn like normal for orbital insertion when the time comes; I usually do this at one-third thrust.

Edited November 4, 2013 by capi3101

[Nao]

Actually, the SSTO rocket would still do 4500 m/s of delta-V for orbit, but you have to be a little more careful about how you pilot it. That's from observation/experience.

That means you didn't push the your designs to the limit. Of course its possible to make SSTO that use as much dV as even most sophisticated asparagus staged performance rocket, but it wou't go much further after reaching orbit. I have done rocket only SSTKE (single stage to kerbol escape) that require more than 16000m/s dV and to ascent with that much energy left, my ship needed more than 5000m/s to get to LKO.

This happens because of two things: 1) Low TWR (1,1-1,2) will make you suffer bigger gravity losses no matter what, while giving more dV. 2) Switching to only nuclear engines as fast as possible at high altitude. Because it's more fuel efficient to burn at an angle with LN-N's than using other engines in the velocity vector direction, and burning at an angle "wastes" dV.

[capi3101]

That means you didn't push the your designs to the limit. Of course its possible to make SSTO that use as much dV as even most sophisticated asparagus staged performance rocket, but it wou't go much further after reaching orbit.

Of course not - but then again, when it comes to just the booster itself, the only place I want to go is LKO. The payload can do the rest of the work.

IIRC, the most I've lifted with an SSTO rocket was somewhere in the neighborhood of 25 tonnes - which was for a payload capable of sending three Kerbals on a Moho flyby.

Hell, did y'all think I was including the payload? I mean, the shoot the whole thing into space as one big piece with no decouplers whatsoever? No way...