Mathematical relationship between gravity and thrust in KSP?

[Themohawkninja]

What is the mathematical relationship between the gravity of a body in KSP, and the thrust needed to keep an object weightless against that body? I want to use this to find out what the minimum amount of thrust it takes to get off of a body (at sea level) in KSP.

[SkyRender]

I believe you're referring to the Thrust to Weight Ratio, which is the exact same as in real life: Thrust to Weight = Thrust divided by mass times local gravity. You can find a lot more useful info at the KSP Wiki.

[ROFLCopter64bit]

TWR Ratio = Thrust / Weight. (Weight is mass * grav constant)

Grav constant changes with each celestial body (and gravity)

The TWR ratio should stay above 1 to actually move.

[Themohawkninja]

Ah, so the units are the same. I thought that maybe the units were different, so you can't use the real-life equation. Thanks for telling me that they are the same!

[ROFLCopter64bit]

Ah, so the units are the same. I thought that maybe the units were different, so you can't use the real-life equation. Thanks for telling me that they are the same!

If you were wondering, the units are:

Thrust = Kn (Kilonewtons)

Mass = T (Metric Ton)

Weight = Kg (Kilogram)

[purpletarget]

SkyRender has it right.

The minimum thrust to hover is at a TWR of 1. That depends on the Thrust (kN) being equal to the Weight (kN) of your spacecraft, which can be found with a simple F=mg calculation where m is the mass (Metric Tons) of your spacecraft, and g is the local acceleration of gravity (m/s^2). (Which itself is variable, as it falls off exponentially as you climb away from the surface)

In addition to the wiki, I've also been taking a stab at a resource that you might find useful in this thread.

[ROFLCopter64bit]

SkyRender has it right.

Well, I'll stop providing useful info.

[Spatzimaus]

purpletarget was correct. Weight is in kN, mass is in metric tons (where one ton equals 1000 kg). All you need to do is have your thrust be higher than your weight; both will be in the same units, as long as you know the local gravity. The physics in this game is the same as in real life; it's just the scale that's different, with the planets and sun having radii about 1/10th that of the real bodies, but with densities about 10 times higher to give comparable surface gravities.

(Which itself is variable, as it falls off exponentially as you climb away from the surface)

Correct, although realistically you'd have to be really high up before it becomes a noticeable difference. On Earth, for instance, the radius of the planet is 6371km, so the gravitational acceleration 200km up is only about 6% lower than it is at the surface; your TWR in low orbit will be almost the same as it would be at sea level. Kerbin's a much smaller planet (only 600km in radius), so it drops off quite a bit faster, but it still means that you have to basically get out of the atmosphere before TWR starts rising noticeably from this.

Now, if you really care about TWR, I recommend downloading the Flight Engineer mod. It tells you your maximum TWR, your TWR at the current throttle level, and what your TWR would be on the planet's surface. It also tells you your current mass as well as the amount of delta-V you have remaining, both of which are useful for spaceplanes.

[Supernovy]

(Which itself is variable, as it falls off exponentially as you climb away from the surface).

Actually, it's not exponential, it's proportional to the inverse square of distance.

[SZDarkhack]

Weight = Kg (Kilogram)

Weight is a force, so it's measured in Newtons (or kN or MN or whatever multiple). Kg measures mass (1T = 1000kg), NOT weight.

[honolululu]

Actually, it's not exponential, it's proportional to the inverse square of distance.

Which is an exponential expression as far as I know.

From http://en.wikipedia.org/wiki/Exponential_function

"Sometimes the term exponential function is used more generally for functions of the form cb^x, where the base b is any positive real number, not necessarily e. See exponential growth for this usage.

In general, the variable x can be any real or complex number, or even an entirely different kind of mathematical object; see the formal definition below."

Although by that definition y=cb^1 is an exponential function.

[SZDarkhack]

Which is an exponential expression as far as I know.

From http://en.wikipedia.org/wiki/Exponential_function

"Sometimes the term exponential function is used more generally for functions of the form cb^x, where the base b is any positive real number, not necessarily e. See exponential growth for this usage.

In general, the variable x can be any real or complex number, or even an entirely different kind of mathematical object; see the formal definition below."

Although by that definition y=cb^1 is an exponential function.

Exponential functions are of the form y=Ca^x, as you said. Notice that x is not a parameter, it's the independent variable (i.e. the function is y(x)). It needs to be in the exponent for the function to be exponential. The inverse square is Cx^(-2), which as you can see is not an exponential, but rather a polynomial function since x is not in the exponent.

[ROFLCopter64bit]

I feel stupid. Thanks guys for making this more clear.

[architeuthis]

As an addendum, if you're in space rather than on the surface of a planet, the relationship between gravity and thrust is that old standby: Newton's second law, F=m*a where F is the thrust of your rocket, m is its mass, and a the acceleration of the vehicle (which happens to be the same thing as is the gravity felt by any Kerbals on board).

[PlonioFludrasco]

Anyone knows the value of the appropriate initial thrust to weight ratio to climb from Kerbin with the optimal climbing rate(reported on the wiki)?

[Z-Man]

TWR=2 is the simple answer that is not wrong enough to argue about.

[Sof]

Anyone knows the value of the appropriate initial thrust to weight ratio to climb from Kerbin with the optimal climbing rate(reported on the wiki)?

Initial TWR around 2, but once you get out of the lower atmosphere and have started your gravity turn in earnest, go as fast as you can.

[PlonioFludrasco]

Thanks! An optimal TWR was the main issue of my rockets, I'll try if with TWR=2 I can build more efficient ones

[PlonioFludrasco]

Initial TWR around 2, but once you get out of the lower atmosphere and have started your gravity turn in earnest, go as fast as you can.

It isn't better to set throttle to adjust speed a little below terminal velocity? (As a guy shows here)

EDIT: never tried personally because, for wrong TWRs, i never catched a terminal velocity ascent

RE-EDIT:ok, for flying at terminal velocity above 10000m full throttle is not enough (Jeb probably would try it using MOAR BOOSTERS!!!), so Sof you are right and I'm a troll.

And climbing vertical before gravity turn at terminal velocity seems quite efficient.

Edited January 9, 2014 by PlonioFludrasco