Learning how to physics

[Rusty6899]

I finished unlocking the tech tree yesterday. I realise it has been a while, but I set myself the constraint of not sending any one-way manned missions.

I was thinking that now I should really learn a bit about designing efficient rockets (at the moment I generally just rehash the same, massive tapering rocket, which I am confident can land me on any solid body in the game, but will cost a king's ransom once money becomes an issue). There were a few things I was wondering, mainly about Delta-V and TWR.

The way I see it, TWR should only be relevant in sub-orbital flight, where T > mg or else you won't budge / will decelerate if in the air.

And; acceleration=(T-mg)/m.

I have heard people on here talking about TWR in orbit, but my understanding was that you are weightless in orbit and your thrust/mass ratio is relevant (g=0 in the above equation).

As for Delta-V,

The impression that I have is that the Delta-V of a rocket is the total change in velocity that the rocket can experience as a result to engine thrust (maybe not a textbook definition, but I'd say it was close enough for now). I am comfortable with this concept and the calculation of it, for orbital flight, but I don't really see how the Tsiolkovsky rocket equation can be applicable when ascending to orbit.

The way I see it, even if you calculate a very large Delta-V, if your TWR > 1, or even just above 1, you will never get to orbit (Delta-V seems to be independent of thrust). Are there any extra equations that are necessary for designing a rocket to reach orbit, or at least rule of thumb concerning TWR for ascent?

One final thing is atmospheric drag, does this have further effects on the Delta-V calculated using TRE or is atmospheric drag the cause of Isp reductions at low altitudes (meaning that it is already factored in).

Edited November 20, 2013 by Rusty6899

[Jason Patterson]

TWR in orbit - This becomes important because orbital maneuvers need to be predictable. If you want to go from Kerbin to Duna, you need to make a particular burn to get there. Assuming you're in a parking orbit around Kerbin, the most efficient burn is going to happen at one instant in your orbit. With a real rocket, it is spread out over time. If that time is relatively brief compared to your orbital period, it is a good enough approximation of instantaneous that only very minor fudging is required to fix the burn from its idealized version. With a very long burn time (TWR<<1) the burn is spread out over a significant fraction of the orbit. This results in a very messy, difficult to predict burn. Further, it wastes much of the Oberth effect's ability to optimize your burn. By burning while slowing down you're losing out on maximum energy per delta-v. You can minimize that by making several small burns and gradually kicking yourself into higher and higher orbits, but in the end you'll have to commit and make a transfer burn, and if nothing else, your real life time is worth something here...

In order to get into orbit your ship must accelerate to some velocity and ascend above the atmosphere (or at least the top of the mountains.) That change in velocity and the delta-v associated with the altitude change are the most basic parts of delta-v for ascending to orbit. If you're familiar with the impulse-momentum theorem, you can consider all forces acting in the rockets direction of motion as applying an impulse to it (F dt) and that impulse creating an associated change in momentum (m dv). That's where things like wind resistance can translate into a delta-v. The constant backward impulse from wind resistance equates to a loss in momentum that your rocket engines have to compensate for. The component of gravity that is in the direction that the rocket is traveling does the same (thus the concept of gravity drag and why we make gravity turns while burning.)

I can only assume you meant TWR<=1 rather than TWR>=1. If that is the case, then yes, you're right. TWR = 1 is the case for thrust balancing weight. Anything higher and it is (at least theoretically) possible to go arbitrarily high/fast. For ascents you're typically looking for a TWR = 2. That seems to be a good balance of upward thrust and economy of scale. On planets with atmospheres it also is the most efficient way to ascend - always moving upward at terminal velocity. Once you start a gravity turn it becomes less important. For planets without an atmosphere bringing along a smaller engine (lower TWR but less total mass and greater delta-v as a result) is often a better option, but you don't want to go much below 1.8 or so for an ascent or you'll lose a bunch of delta-v to gravity drag.

TWR = 2 includes drag. Isp is lower in an atmosphere because the gases being ejected from the rocket nozzle are blocked by the air outside the nozzle. They can't exit freely, at full speed, so the rocket is less effective.

[capi3101]

The way I see it, TWR should only be relevant in sub-orbital flight, where T > mg or else you won't budge / will decelerate if in the air.

And; acceleration=(T-mg)/m.

I have heard people on here talking about TWR in orbit, but my understanding was that you are weightless in orbit and your thrust/mass ratio is relevant (g=0 in the above equation).

Two bad assumptions there:

1) Your mass is not constant, ergo your acceleration formula is invalid. It could be if you take it down one more notch and get into the physical concept of jerk, the change in acceleration in time, which would account for your change in mass.

2) G in orbit is not zero. It's just not 9.81 m/s² anymore. Probably a good thing, too...a ship with an infinite/undefined TWR (which matematically is what you would get in the case TWR = T / Mg where g is zero) would shoot off like a bat out of hell; it'd accelerate so fast there's no way its structure would be able to handle it.

To calculate g at a given orbital radius, take the gravitational parameter of the world (which is just the gravitational constant G=6.67*10^-11 times the mass of the planet) and divide it by the distance (in meters) to the center of the planet's core (i.e. the planetary radius + the altitude of the orbit).

As for Delta-V,

The impression that I have is that the Delta-V of a rocket is the total change in velocity that the rocket can experience as a result to engine thrust (maybe not a textbook definition, but I'd say it was close enough for now). I am comfortable with this concept and the calculation of it, for orbital flight, but I don't really see how the Tsiolkovsky rocket equation can be applicable when ascending to orbit.

The way I see it, even if you calculate a very large Delta-V, if your TWR > 1, or even just above 1, you will never get to orbit (Delta-V seems to be independent of thrust). Are there any extra equations that are necessary for designing a rocket to reach orbit, or at least rule of thumb concerning TWR for ascent?

Well, you kinda have to spend fuel to make a rocket work; that's kinda fundamental to their operation. In that alone, the Tsiolkovsky Equation is <channel_doctor_strangelove>not only possible...it is essential!!!</channel_doctor_strangelove>

No extra equations are necessary for calculating how to reach orbit. Most folks will tell you to shoot for an initial stage I_sp of 1.6-1.7, with the idea being that the average TWR for the stage from the time it lights to the time it runs out of gas is around that magic 2.0-2.2 range (where thrust, gravity and drag are optimally balanced). I find for planning purposes that if you take your payload for the stage and divide it by .04, you get the amount of thrust that stage is going to need to have a TWR in that general vicinity. You then plan your engine cluster accordingly, add it to the payload mass, add the mass of everything else involved with the stage except the fuel tanks, and then you work Tsiolkovsky backwards to figure out how much fuel you're going to need (I did a rather thorough example of this just recently). Get as close as you can to that amount of fuel, then work Tsiolkosky forward to see how well you did on the stage delta-V. You wind up with the total mass of the rocket so far at that point, and can go back to check to see how well you did with the TWR.

One final thing is atmospheric drag, does this have further effects on the Delta-V calculated using TRE or is atmospheric drag the cause of Isp reductions at low altitudes (meaning that it is already factored in).

The rocket equation does not account for drag; there are no factors in it to account for it. That's the main reason why, on Kerbin at least, it takes 4,550 m/s of delta-V to get to orbit and at the end you're going ~2,250 m/s - the other ~2,300 is lost to fighting gravity and drag.

[Rusty6899]

Surely when accelerating when in orbit, your acceleration at a given moment is T/m (from Newton's second law), assuming that you are accelerating directly prograde/retrograde? When ascending from a point on the ground, you are counteracting gravity, but when in orbit, the inertia of your orbit is negating your weight, so weight doesn't need to be considered.

I assume that the mass flow rate of a tank is constant for a rocket in orbit, so the total delta-v of a stage would be approximately T*t/((m2+m1)/2). The average thrust/mass ratio multiplied by the time of the burn.

I hadn't actually meant to say that the Tsiolkovsky rocket equation wasn't applicable, just that I din't see how it was sufficient. With a TWR of 2 it all makes sense though.

Thanks for all the help anyway, I should be well on my way now.

[capi3101]

Newton's second law is not directly applicable if mass is not constant (see "Variable-mass systems").

The Rocket Equation is Newton's Second Law, modified to account for the variable mass.

[Geschosskopf]

...With a very long burn time (TWR<<1) the burn is spread out over a significant fraction of the orbit. This results in a very messy, difficult to predict burn. Further, it wastes much of the Oberth effect's ability to optimize your burn. By burning while slowing down you're losing out on maximum energy per delta-v....

Please correct me if I'm wrong but it's my understanding that the Oberth effect depends on the mass flow rate of the exhaust stream. The higher this is, the more benefit Oberth gives you and vice versa. Thus, Oberth is the most help to chemical rockets, makes only an infinitesimal difference to ion engines, and has only a small effect on nukes. Because long burn times come from the low-thrust nuke and ion engines, which Oberth doesn't really help anyway, it doesn't look like you're losing out on Oberth simply by having a long burn time. Because of this (and because I'm sick and tired of waiting through 5-10minute ejection burns), I've lately taken to using a chemical ejection stage.

[Sirrobert]

Please correct me if I'm wrong but it's my understanding that the Oberth effect depends on the mass flow rate of the exhaust stream. The higher this is, the more benefit Oberth gives you and vice versa. Thus, Oberth is the most help to chemical rockets, makes only an infinitesimal difference to ion engines, and has only a small effect on nukes. Because long burn times come from the low-thrust nuke and ion engines, which Oberth doesn't really help anyway, it doesn't look like you're losing out on Oberth simply by having a long burn time. Because of this (and because I'm sick and tired of waiting through 5-10minute ejection burns), I've lately taken to using a chemical ejection stage.

The effect of the Oberth effect is simple: Acceleration is most efficient at Periaps, and deceleration is most efficient at Apoaps

Having a to low TWR in space won't prevent you from accelrating, but it will make your accelration extremely slow, and even without the Oberth, noone wants to burn for 20 minutes.

Count an Orbital period of 40 minutes, and you'd be pointing the other way than when you started if you burn prograde

[Jason Patterson]

Please correct me if I'm wrong but it's my understanding that the Oberth effect depends on the mass flow rate of the exhaust stream. The higher this is, the more benefit Oberth gives you and vice versa. Thus, Oberth is the most help to chemical rockets, makes only an infinitesimal difference to ion engines, and has only a small effect on nukes. Because long burn times come from the low-thrust nuke and ion engines, which Oberth doesn't really help anyway, it doesn't look like you're losing out on Oberth simply by having a long burn time. Because of this (and because I'm sick and tired of waiting through 5-10minute ejection burns), I've lately taken to using a chemical ejection stage.

That's pretty much what I wrote, with a few small changes.

Oberth relies on two things:

Rockets work by changing a vessel's momentum.

The size of an orbit is changed by changing a vessel's energy.

Burning at or near periapsis always is beneficial compared to not burning there. The difference is the number of times you would have to orbit a body to do stepwise burns at periapsis to get the total delta-v you need. Mass flow rate doesn't have anything to do with it, except in regard to Isp and producing thrust. Higher TWR makes it more practical and lets you do it in a single burn instead of a series, but it is definitely possible to do a dozen separate burns at periapsis that all add up to a single strong burn.

[Jason Patterson]

deceleration is most efficient at Apoaps

I'm not sure what you mean. If you mean that it is most efficient to lower your periapsis by burning at apoapsis, I agree, but in general you want to slow down (ex: for landing) at the periapsis for the exact same reason that you want to speed up there. Changing direction can also be done very cheaply at apoapsis.

[Kasuha]

Oberth effect has nothing to do with periapsis or rockets using chemical propellant.

Oberth effect just means that with given accelerating force (thrust), object's kinetic energy is growing the faster the faster the object is already moving.

See: Oberth Effect (Wikipedia)

In orbital meachanics the object is usually moving the fastest at the periapsis. That's where the periapsis comes from.

And usefullness for chemical propellants only comes from the fact that these engines can provide short powerful bursts, utilizing the Oberth effect better. But there is nothing preventing ion-propelled probes to use Oberth effect too, they just won't gain that much from it.

Edited November 14, 2013 by Kasuha

[Alistone]

Rusty, you are generally correct; T/W only "really" matters in suborbital flight.

BUT:

A higher T/W ratio will allow you to take better advantage of the oberth effect for ejection and capture burns. Essentially you can get more of your "burn" done closer to periapsis (lower in gravity well) which adds oberth effect efficiency.

Also, for LONG burns you'll lose your mind if you actually have to wait several hours for you "ion engine powered" probe to complete a burn. You "can", but generally it is much easier for your gameplay if you aren't sitting idly for 40 minutes while your ultra low T/W ratio craft completes its ejection burn.

[Alistone]

And for your latter question about optimal T/W ratio for ascent:

Try to have a T/W ratio of 1.5 to 2 for the first half of your fuel; after 12,000m the higher the better.

It varies a lot by craft, but on my more massive ships I tend to be slightly lower (I suffer more gravity losses and slightly less air resistance losses; BUT my "max Q" is less because I'm traveling slightly slower throughout the ascent meaning my ship tends to stay in one piece rather than breaking apart).

Often people put extra or larger rockets on the center stack to help T/W improve later in the ascent.

Really you are trying to match terminal velocity at each altitude; if you are going too fast then add more fuel. If you are going too slow then cut back on fuel or add more engines. Trial and error will get you where you want to go.

[Geschosskopf]

Oberth effect has nothing to do with periapsis or rockets using chemical propellant.

Oberth effect just means that with given accelerating force (thrust), object's kinetic energy is growing the faster the faster the object is already moving.

See: Oberth Effect (Wikipedia)

You might want to re-read that article. That's where I learned that it only really helps chemical rockets, and that's because of their high mass flow rate.

Technically speaking, Oberth has absolutely nothing to do with orbital mechanics; it's a separate thing that is only about how rocket engines work. Oberth merely states that the faster a rocket is moving, the more fuel-efficient its engine runs, as in getting more delta-V per unit of fuel. This happens whether the rocket is accelerating in a straight line or following a curved path around a planet. But this effect comes from the momentums of the rocket and the exhaust stream, and the exhaust stream's momentum is pretty much its mass flow rate. Momentum is mv, so mass is just as important as velocity. This is why Oberth only really helps chemical rockets. Ion engines have huge exhaust velocities but are moving only trace amounts of mass at any given time, so their mass flow rates are very low. This is why you can put such a small fuel tank on an ion probe and do a grand tour with it.

Now, if you're on a tight fuel budget, you can combine Oberth OT1H and orbital mechanics OTOH to save some fuel. Orbital mechanics, not Oberth, is what makes a rocket move faster at Pe than anywhere else. Oberth, not orbital mechanics, is what makes Pe burns more fuel-efficient than burns elsewhere. But this is only really applicable to fly-bys on open orbits, like say Voyager. If you're in a closed orbit and want to stay there, then all you're doing at Pe is adjusting your Ap. And you're only going to make an Ap adjustment at Pe anyway, whether or not Oberth does anything for the type of engine you have.

Or so it seems to me.

[UberFuber]

TWR (or technically, the mass of your ship) is very important if you want to enter orbit around a planet (especially planets without atmosphere). If you're TWR is woefully low, you might sail right past the planet's SOI before you can decelerate enough to enter orbit.

[Kasuha]

You might want to re-read that article. That's where I learned that it only really helps chemical rockets, and that's because of their high mass flow rate.

I have read that article rather carefully.

... thus the Oberth effect is often far less useful for low-thrust reaction engines such as ion drives, which are limited in their ability to generate a large amount of impulse in a small amount of time.

Far less useful does not mean useless.

Now, maybe it's time for you to read that article more carefully. Because Oberth effect is not about delta-v. It is about kinetic energy of the ship. It has nothing to do with propulsion method. It's a consequence of how kinetic energy is calculated - E=(m.v^2)/2. Assuming unit mass of the ship (1 kg), if your velocity is 1 m/s and it grows to 2 m/s, your kinetic energy grows from 1/2 J to 4/2 J, i.e. by 3/2 = 1.5 J. If your velocity is 10 m/s and grows to 11 m/s, your kinetic energy grows from 100/2 J to 121/2 J, i.e. by 21/2 = 10.5 J.

That's the matter of Oberth effect.

Edited November 15, 2013 by Kasuha

[Nao]

And for your latter question about optimal T/W ratio for ascent:

Try to have a T/W ratio of 1.5 to 2 for the first half of your fuel; after 12,000m the higher the better.

It varies a lot by craft, but on my more massive ships I tend to be slightly lower (I suffer more gravity losses and slightly less air resistance losses; BUT my "max Q" is less because I'm traveling slightly slower throughout the ascent meaning my ship tends to stay in one piece rather than breaking apart).

Often people put extra or larger rockets on the center stack to help T/W improve later in the ascent.

Really you are trying to match terminal velocity at each altitude; if you are going too fast then add more fuel. If you are going too slow then cut back on fuel or add more engines. Trial and error will get you where you want to go.

I thought that for a long time, but now i think the opposite. The higher you go the lower the TWR should be, that's because right after starting gravity turn the importance of TWR diminishes quite fast, and if we have less engines (lower TWR) more of the fuel energy is transfered to payload itself, making the launcher more mass efficient.

The thing is, while flying vertical at terminal velocity is the most fuel efficient method for given craft, after we get to some vertical speed (enough to coast out of thick atmosphere) gaining more will only net us losses. That's why we do gravity turn but then if we turn the ship at an big angle to velocity vector, we get big steering losses, and if we try to avoid that by starting it early we get increased drag losses. In the end the most efficient way is actually to "coast" at low thrust (flying below terminal velocity) until we fly more horizontally.

Then comes the second part where thrust is important as we accelerate semi horizontally, but it ends quickly as we gain orbital velocity, lowering the gravity drag. And since we still have a lot of vertical speed stored accelerating fast in middle atmosphere only increases drag losses.

At this point the difference between accelerating fast and slow doesn't bring us much improvement. And if we bring less engine mass up there, it means we have saved a lot of fuel (more than we would have gained from more efficient - high TWR flight profile).