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# Delta-V or TWR on takeoff?

## Question

I am building a rocket, just a simple one to rescue a few kerbals stuck on a broken space station, and I wanted to ask.

On takeoff (first stage) is dV or TWR more important? I can choose to add two small liquidfuel boosters to the side of my rocket that increase TWR, but decrease dV. Should I include them or leave them off? Thanks for the help,

Luke

Edited by Saltless Lemons

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Ummm. Yes.

It depends on the numbers. What is your TWR with and without the boosters and what is your delta V with and without the boosters?

You need TWR to get off the ground. Technically speaking your craft won't leave the ground without a TWR of 1 or higher. However exactly 1 is crawling off the launchpad. I shoot for 1.25 to 1.5. Too much TWR and you will go fast which makes it hard to turn in the air and you may run into shock heating too. Remember, it's thrust to weight ratio, not thrust to mass ratio. Your weight changes as you get further from the center of gravity so that means the higher you go, the more your TWR increases. SO, the launchpad is the lowest TWR you will have on a single stage rocket at full throttle. You can use this to your advantage because you only need to design for the launchpad. However, if using a multistage rocket, it gets a little more tricky. You want to make sure the upper stage has enough TWR at the altitude it will be working alone. Because it is an upper stage, it can have less than 1 on the launchpad.

You need Delta V to reach your destination. Depending on your piloting skills you can reach orbit around 3400 Delta V on Kerbin (Atmospheric Button enabled if in Kerbal Engineer). If you aren't as good a pilot you may need a few hundred more.

Both are important, you can't really compare them that way. It's like asking if you want more horsepower or more gasoline in your car.

Edited by Alshain

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Neither. On the first stage the pressing concern is either mass or cost.

If you're working in an early career, you may be dealing with a pad mass restriction where the cheapest solution is too heavy to launch. If not, you want to do the mission as cheaply as possible to save money for more lucrative missions down the road.

T/W and DV are not competing criteria. You must achieve absolute minimums on both, and having an excess on one will not overcome a deficiency of the other. I design my booster stages to achieve both 1.4 t/w *and* 1,800 m/sec DV.

Best,

-Slashy

Edited by GoSlash27

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T/W and DV are not competing criteria. You must achieve absolute minimums on both, and having an excess on one will not overcome a deficiency of the other. I design my booster stages to achieve both 1.4 t/w *and* 1,800 m/sec DV.

For practical purposes yes, but to be pedantic: an excess of one does reduce the minimum of another. A small portion of the dV cost to orbit (a couple hundred m/s) is gravity losses establishing a gravity turn. It well known that higher thrust ratios reduce those losses. Conversely, a lower TWR needs more dV to sink into those losses. The relationship is asymptotic though, so don't try to compensate for one with the other.

TWR and dV are both derived values. They are also connected via the fuel mass. Too many variables feed into them to make them useful design parameters (though they make awesome requirements). If you are building a new ship, start with the payload. Reducing the orbiter to a bare minimum of mass ripples through your design. The rocket equation teaches us that each pound shed from the payload gives exponential savings.

Edited by ajburges

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I can choose to add two small liquidfuel boosters to the side of my rocket that increase TWR, but decrease dV.

Adding boosters should increase both dV and TWR, generally speaking. May we see a picture of the rocket in question?

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Remember, it's thrust to weight ratio, not thrust to mass ratio. Your weight changes as you get further from the center of gravity so that means the higher you go, the more your TWR increases.

Uh, what? I think you have some misconceptions.

It's technically true that you get lighter as you ascend, but not as much as you think. The acceleration due to gravity at LEO is 7.8m/s2, 80% of that at sea level. TWR increases during a flight primarily because you burn fuel and get lighter, not because you're getting higher!

Secondly, TWR is useful as a measure of how much acceleration your ship can pull normalised to multiples of kerbin's (or other reference body's) gravity (at sea level). It doesn't change with altitude. On Kerbin it's basically synonomous with TMR. It's specified as weight rather than mass because weight is easy to measure (IRL) and gives you an instant indication of whether you'll be able to take off from whatever body you're on.

Weight becomes totally irrelevant once you stop burning with a radial component. It's all about mass.

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TWR and dV are both derived values. They are also connected via the fuel mass. Too many variables feed into them to make them useful design parameters

Actually, that's not true.

I design every stage I build this way. Scope out my tutorial here: http://forum.kerbalspaceprogram.com/threads/136367-How-to-mathematically-design-stages for how the math works.

Best,

-Slashy

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To understand this completelly you need to understand how the rocket equation works. I'll give a quick summary here, following this lecture.

First of all the rocket equation is:

$\Delta V = V_e \ln \left( \frac{m}{m_0} \right)$

The basic underlying differential equation that describes the system is:

$m\frac{dv}{dt}=-v_e\frac{dm}{dt}$

This system however does not take into account any external force acting on the craft. Adding to the equation a simple coefficient for the gravity is trivial (notice this is not complete as it considers gravitational acceleration equal independent of the altitude). - Note that once you are in free fall the gravitational acceleration drag is by definition zero, as it evens out with the kinetic energy to provide your orbit. So this is only while you are still not in orbit.

$m\frac{dv}{dt}=-v_e \frac{dm}{dt}-mg_0$

This can still be solved easily, one would get then:

$\Delta V=V_e \ln\left(\frac{m}{m_0}\right)-g_0 t_b$

(small note: above equation is only correct if TWR > 1, if thrust to weight is less than one, you keep standing on the platform and there is a normal force that prevents you from falling).

And here an interesting term surfaces: the total time of burning the fuel. - We also see that our effective delta-V reduces the longer the burn time. Time of burn one can combine directly with Trust to Weight ratios: a higher TWR means that one needs to burn less time to provide the same change in acceleration (standard newton). Thus higher TWR are better: near infinite TWR (a cannon ball) is the best, right?

Guess not!

There is another very important force you cannot forget on earth/kerbin when lifting off. The atmospheric drag. And a high TWR means a high acceleration & speed in a dense (low altitude) atmosphere. This then leads to more loss due to atmospheric drag. One can easily modify the differential equation once again:

$m\frac{dv}{dt}=-v_e \frac{dm}{dt}-mg_0-D$

The drag force however (as we said) can't at all be considered constant, so the drag equation has to be used. Now this is a hard point in KSP; does KSP finally use the normal drag equations instead of something utterly ridiculous based on mass??? - Some verification of other people is handy.

Anyway considering it use the realastic drag equation:

$D=\frac{1}{2}\rho v^2 A C_D$

Where everything is constant apart from the velocity & the density (C_D is a value that needs to be given for each rocket, and A is the cross-section area/surface area corresponding to this C_D).

Now there are many many approximations for the density in the standard atmosphere on earth, and I have no idea what KSP uses (linear, quadratic, an exponential curve like on earth...)? But this equation could then be filled into the differential equation, and that one could be solved once again.

Anyways, it is important to see that the atmospheric drag increases with the square of the velocity: and hence very high speed (and thus TWR) might actually be bad near launch. Now for earth based rockets, with a TWR of 2-3, the atmospheric drag losses are typically in the order of 5% of the gravitational drag losses; Structural integrity & equipment protection simply put a hard limit on the maximum TWR that can be achieved.

Edited by paul23

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...

Depending on your piloting skills you can reach orbit around 3400 Delta V on Kerbin (Atmospheric Button enabled if in Kerbal Engineer). If you aren't as good a pilot you may need a few hundred more.

...

LKO is 3200m/s (calculated with VAC ISP, using reasonable engine)

3400 is a comfortable margin for error.

With a Mammoth, you can go to space with 3000m/s ASL ISP (maybe 2900?), even less with a Mainsail.

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LKO is 3200m/s (calculated with VAC ISP, using reasonable engine)

3400 is a comfortable margin for error.

With a Mammoth, you can go to space with 3000m/s ASL ISP (maybe 2900?), even less with a Mainsail.

I disagree.

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I disagree.

With what ?

I go to space with a launcher with dV=3200m/s (VAC). On the launch pad KER says it's even around 3000 (KER uses ASL dV). If I use 3400m/s (VAC) in my designs, it's only because I'm deorbiting the recoverable stage and land it around KSC (with a powered landing).

Of course if you use a non streamlined payload, you'll need 100 or 200m/s more.

Or, I misunderstood what you wrote.

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From what I've been seeing, for TWRs around 1.3 or less you start to spend more dV to get to orbit, quite independently of one's piloting skills.

In my experience in situations where the TWR would otherwise be low yet enough for liftoff, it's often better to replace a Skipper engine with a Mainsail, even thought the latter adds 3t (and thus reduces dV), because you end up using less dV to get to orbit.

I suspect this is the result of a similar mechanism to why in 0.9 one tried to get a TWR that resulted in the ship ascending at close to Terminal Velocity: to get out of the gravity well (and from paying the fuel price of simply fighting gravity) as fast as possible but not so fast that the losses due to aerodynamic drag were larger than the gains from it.

In 1.0 and the new drag model, means that Terminal Velocity is near impossible to reach, but in the lower atmosphere there is a vast increase in aerodynamic drag losses at hypersonic speeds (when there are flames around the ship) so one tries to ascend through the first 30km or so just below the level at which flames start to appear but otherwise as fast as possible, and that sits at around the 1.3 - 1.5 range for TWR in the launchpad.

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Gotta keep in mind that minimal DV expenditure isn't profitable. You can have a stage that expends more DV but weighs less overall by reducing the t/w ratio. You can go even further and make a cheaper stage at the expense of DV *and* fuel consumption.

Minimal mass and minimal cost are worthwhile goals when designing stages. Minimal DV expenditure isn't.

Best,

-Slashy

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I go to space with a launcher with dV=3200m/s (VAC). On the launch pad KER says it's even around 3000 (KER uses ASL dV). If I use 3400m/s (VAC) in my designs, it's only because I'm deorbiting the recoverable stage and land it around KSC (with a powered landing).

I underlined the important parts of that sentence that your first comment failed to include.

LKO is 3200m/s (calculated with VAC ISP, using reasonable engine)

3400 is a comfortable margin for error.

With a Mammoth, you can go to space with 3000m/s ASL ISP (maybe 2900?), even less with a Mainsail.

Implies that is how it is and should be for everyone. I disagree. GoSlash explained why so I won't bother repeating it. The fact you quoted me implies you were either discussing what I said, which you didn't seem to offer context to indicate that, or you were correcting something I said, which you weren't because what I said was not wrong.

Edited by Alshain

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...does KSP finally use the normal drag equations instead of something utterly ridiculous based on mass??? - Some verification of other people is handy.

KSP has always used the correct drag equation, at least since IÃ¢â‚¬â„¢ve been playing (starting with 0.23). The problem was that A was calculated as a function of, and directly proportional to, m. The formula used resulted in ridiculously high values for A, thus unrealistically high drag. The formula was such that all vehicles, regardless of shape, had, as I recall, a ballistic coefficient of 625.

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Well no, what was also weird was the way Cd was calculated. This resulted in the fact that it doesn't matter how you shaped (stacked) object.

The drag was just a function of an object should be based on it's lift (induced drag). And the skin/form drag, oh and of course the shock-wave drag, but I'd forgive KSP for not using that - it's currently near impossible to predict drag for those regions given a shape anyways.

C_D hence depends on C_D0 & C_Di, where C_Di can be calculated directly from the lift. But C_D0 needs to be simulated, given a the full body. Oh notice that A is just a reference for the body, so that the same body can easily be scaled. The factor for different angles is part of the induced drag, up to a ~45 degrees angle, after which the lift & drag directions change, and you'll have to use a different C_D0.

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I like to have a liftoff TWR ratio somewhere in the range of 1.2 to 1.5. This results in fairly high gravity losses, but thatÃ¢â‚¬â„¢s acceptable to me. Setting as the goal of your design Ã¢â‚¬Å“lowest ÃŽâ€v to orbitÃ¢â‚¬Â results in vehicles that are mass and cost inefficient. IÃ¢â‚¬â„¢d rather expend more ÃŽâ€v in exchange for maximizing the payload that a particular engine can put into orbit.

To understand how this works, letÃ¢â‚¬â„¢s consider an example. Say IÃ¢â‚¬â„¢m launching a payload using a Ã¢â‚¬Å“Twin-BoarÃ¢â‚¬Â as the first stage. The rocket has a total liftoff mass of 100 t, and a liftoff TWR of 1.9. Suppose we find this configuration can put a 20 t payload into orbit while expending 3200 m/s ÃŽâ€v.

Suppose now that everything remains the same but we start adding fuel tanks. Adding fuel tanks increases the mass and drives down the TWR. LetÃ¢â‚¬â„¢s say weÃ¢â‚¬â„¢ve added so much extra propellant that the total liftoff mass is now 150 t, and the liftoff TWR is 1.27. With all that extra fuel to burn we can now lift a much larger payload. However, with a lower TWR we experience greater gravity losses. Suppose we find this configuration can put a 30 t payload into orbit while expending 3400 m/s ÃŽâ€v.

In the second case we find that, using the same engines, we can orbit a 50% larger payload. And since all we did was to add relatively cheap fuel tanks, our cost per ton of payload is significantly reduced. True, we used more ÃŽâ€v, but who cares? The low TWR/high ÃŽâ€v vehicle delivered a larger payload for lower unit cost. IsnÃ¢â‚¬â„¢t that what really matters?

The numbers above are just a made up example, but they are based on actual experience and should be indicative of what youÃ¢â‚¬â„¢ll get in the game.

Edited by OhioBob
fixed formatting

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Everyone please remember to address the questions of the thread, vice get into a debate about who has a better rocket. The question is about dV and TWR, and pics can go a long way toward collaboration.

The drag force however (as we said) can't at all be considered constant, so the drag equation has to be used. Now this is a hard point in KSP; does KSP finally use the normal drag equations instead of something utterly ridiculous based on mass??? - Some verification of other people is handy.

Yes, drag used to have a mass component to it. That's because, at the time, it was easy to use mass as a stand-in for other parameters and likely was simple to code (to get KSP up and running).

The drag system was updated as part of the aero overhaul in 1.0. I won't go into huge details because there are several other threads covering this topic.

However, rocket shape and design does factor in to drag now. This is probably a big reason why people still debate "how much dV to LKO?" Since dV expense to LKO is now also tied to rocket shape and flight profile (due to differences in drag).

Cheers,

~Claw

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Well no, what was also weird was the way Cd was calculated. This resulted in the fact that it doesn't matter how you shaped (stacked) object.

That was weird too, but it wasnÃ¢â‚¬â„¢t the reason for the so called Ã¢â‚¬Å“soupophereÃ¢â‚¬Â. Each part had an assigned Cd, with the total Cd of the vehicle being computed as a mass-weighted average. The Cd varied only slightly from one vehicle to another, with it typically being equal to about 0.2. The bigger problem was the area, which was computed using the formula A = 0.008*m. This basically turned everything into a flying pancake.

The aerodynamics of the design meant nothing. Cd and A where both functions of mass and it didnÃ¢â‚¬â„¢t matter what shape the vehicle had. Drag was computed using the correct formula, but the input variables of Cd and A were bogus. The Cd value was low, so thatÃ¢â‚¬â„¢s not the reason for the ridiculously high drag force. The extreme drag came from unrealistic values of A.

(Claw, sorry if this is off topic. I was writing as you were posting.)

Edited by OhioBob

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I like to have a liftoff TWR ratio somewhere in the range of 1.2 to 1.5. This results in fairly high gravity losses, but thatÃ¢â‚¬â„¢s acceptable to me. Setting as the goal of your design Ã¢â‚¬Å“lowest ÃŽâ€v to orbitÃ¢â‚¬Â results in vehicles that are mass and cost inefficient. IÃ¢â‚¬â„¢d rather expend more ÃŽâ€v in exchange for maximizing the payload that a particular engine can put into orbit.

People keep saying this, but its not true, it CAN'T be true in stock KSP. High TWR rockets are capable of a high enough LKO payload fraction (over 24%) that it would be impossible for a low TWR rocket to make it to orbit even if its fuel tanks and engines had no mass at all (mods with cryo engines might be an exception, as those very much can get to orbit with lower fuel ratio). The cost thing is more complicated and not subject to simple disproof, but that people keep repeating it alongside the mass thing suggests that whoever originated the idea didn't know what they were talking about.

Edited by Requia

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Wouldn't it also matter how quickly your TWR changes and what the max TWR for the stage will end up being? I could have two rockets that both start on the launch pad with 1.4 TWR, but one could end at 3.0 TWR when the stage burns off and the other might end at 4.5 TWR. I would assume that those numbers should fit in somehow to determine the most efficient ascent.

For me personally, I find that anything over 1.5 on the launch pad can be harder to fly and control through the early parts of the gravity turn, while something around 1.35 or 1.4 will be nice and stable. Also, anything over 1.5 and I end up with a relatively large circularization burn because I reach my desired Ap well before I've built up enough speed. A high TWR will build more vertical velocity than you really want because you won't be able to get horizontal as easily. I'm not sure how it compares for a total DV to orbit point of view, but I always feel like I've done poorly if I have a large circularization burn (600+ m/s).

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People keep saying this, but its not true, it CAN'T be true in stock KSP. High TWR rockets are capable of a high enough LKO payload fraction (over 24%) that it would be impossible for a low TWR rocket to make it to orbit even if its fuel tanks and engines had no mass at all (mods with cryo engines might be an exception, as those very much can get to orbit with lower fuel ratio). The cost thing is more complicated and not subject to simple disproof, but that people keep repeating it alongside the mass thing suggests that whoever originated the idea didn't know what they were talking about.

My investigation of the problem suggests otherwiseÃ¢â‚¬Â¦

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My investigation of the problem suggests otherwiseÃ¢â‚¬Â¦

Yeah, same here (although I haven't conducted a rigorous study like the one you've presented here).

I've found my upper stages to be most mass- efficient when designed to have a minimum t/w around 0.7.

For lower stages it's in the neighborhood of 1.3-1.6 depending on the engine, but in most cases right at 1.4.

Of course... since my booster stage is considered disposable and it's weight doesn't cascade down the stack, I almost always use solid fuels for the first stage because they're so much cheaper.

Best,

-Slashy

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My investigation of the problem suggests otherwiseÃ¢â‚¬Â¦

The mass fraction of your mass fraction optimized rocket is worse than what I just said low dv rockets are capable of. Not to mention that it IS a low dv rocket if it really makes orbit (if it does we need to reassess how dv optimization works out). The optimized for cost rocket seems off too, though I've never done cost optimization for 2.5m rockets, I may have to do exactly that. I'm curious if you ever flew these? It shouldn't be possible to fly rocket#3 to orbit as far as I can tell, because thrust vectoring will drop your overall direction of travel thrust very slightly, normally that isn't a huge deal but at 1.03 dropping to 1.02 means losing a third of the dv that theoretically would have provided at launch, alternatively, can you verify that your simulation took it into account?

Yeah, same here (although I haven't conducted a rigorous study like the one you've presented here).

I've found my upper stages to be most mass- efficient when designed to have a minimum t/w around 0.7.

For lower stages it's in the neighborhood of 1.3-1.6 depending on the engine, but in most cases right at 1.4.

Of course... since my booster stage is considered disposable and it's weight doesn't cascade down the stack, I almost always use solid fuels for the first stage because they're so much cheaper.

You don't seem to understand the concept of dv optimization, you don't get a dv boost for having higher TWR on upper stages.

Edited by Requia

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You don't seem to understand the concept of dv optimization, you don't get a dv boost for having higher TWR on upper stages.

Requia,

Clearly I don't, because the entire concept of "dv optimization" is an exercise in futility IMO.

But if you put together a write-up about it, I'll be sure to give it a once-over.

I don't optimize for minimal DV expenditure. I optimize for minimal stage mass in upper stages and minimal cost in lower stages.

Best,

-Slashy

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The mass fraction of your mass fraction optimized rocket is worse than what I just said low dv rockets are capable of.

When you say Ã¢â‚¬Å“mass fractionÃ¢â‚¬Â I assume you are referring to the payload mass fraction. I donÃ¢â‚¬â„¢t really care that much about payload fraction. I care even less about ÃŽâ€v. What IÃ¢â‚¬â„¢m interested in is maximizing the total payload mass that a particular pair of engines can put into orbit. The payload mass definitely goes up when we add on more propellant, though the payload fraction might decrease some. ThatÃ¢â‚¬â„¢s OK Ã¢â‚¬â€œ fuel is cheap, engines are not.

If I have one launcher with a TWR of 2.0 and a payload fraction 0.24, and another launcher with a TWR of 1.4 and a payload fraction of 0.21, IÃ¢â‚¬â„¢ll take the latter. With the same engines, the second rocket will launch 25% greater payload mass.

I'm curious if you ever flew these?

Yes, I experimented with them. The payload capacities that I could attain in the game were a little less than the simulations. I assume this is mainly because I flew less than ideal ascent profiles. The lowest TWR rocket was especially difficult to fly because its extreme slenderness made it rather wobbly. Otherwise it performed alright. I was definitely able to launch much heavier payloads with the larger, low TWR rockets.

Edited by OhioBob

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