How much does TWR in an atmosphere matter. Is TWR < 2 or TWR > 2 better?

[Alchemist]

What I meant by energy gain is how much energy you get per time unit (dW/dt), while the thrust is directly proportional to to the delta v spending F=m*d(Delta v)/dt

Therefore energy gain per thrust unit is equal to energy per Delta v per mass unit (and what we are interested in is energy per mass unit, because we need to get the energy to the payload)

W/(m*Delta v)=(dW/dt)/F=(mgv+mva)/(mg+ma+kv²)

[Northstar1989]

A lot of math in earlier posts here, but I think the ultimate question was what was the most efficient TWR, no?

It's an interesting question, but players debating this point always miss one key point- lift.

Many rockets are equipped with tail fins, which are capable of providing a small amount of lift, and a great deal of drag once the rocket begins its gravity turn (until the prograde vector points at less than 45 degrees to the horizon, the majority of force on the tail fins will be retrograde-horizontal rather than upwards).

Additionally, the same tail fins increase drag if the player points even slightly off the vertical during their initial ascent (that is- they increase the effect of steering losses).

Both factors act to increase the relative effects of atmospheric drag, therefore, the ideal TWR during ascent is actually less than 2 once terminal velocity is achieved.

Another factor KSP players typically forget in this discussion though- the ideal TWR is actually infinite (the higher the better) until the rocket manages to first achieve terminal velocity (most rockets start out stationary). Up until that point, you are moving at less than ideal speed (terminal velocity), and the faster you can catch up to terminal velocity the better.

Finally, your ideal TWR goes down AGAIN once you start your gravity turn, if atmospheric drag is non-negligible at that altitude (otherwise, you will end up moving through the atmosphere at a speed greatly exceeding terminal velocity, and your path-length through the atmosphere has also increased vs. a "straight up" ascent). And you SHOULD start your gravity turn early (by around 12500 meters), and make it very gently/slowly, rather than attempting it all at once higher up (which poses both control issues and efficiency issues)

Therefore, a BETTER TWR PROFILE (than TWR = 2 all the way up) would look more like this:

Launchpad: TWR = 3 (best achieved with short-lived SRB's, such as custom ones from ProceduralParts mod with very low burn-times)

1000 meters TWR = 2 (terminal velocity should be nearly achieved by around this point- SRB's should be shed slightly before terminal velocity)

3000 meters: TWR = 1.92 (steering losses are going to cause a rocket to exceed terminal velocity, and create excessive drag from the tail fins)

5000 meters: TWR = 1.94 (steering losses become less of an issue as the rocket has more momentum in the proper direction)

8000 meters: TWR = 1.96 (steering losses less important still, thinning atmosphere having less impact on tail fins)

10000 meters: TWR - 1.98 (trends continue)

12500 meters: TWR = 1.94 (at this point, you should begin your gravity turn: so ideal TWR declines)

15000 meters: TWR = 1.84 (gravity turn becomes steeper, so TWR necessary to maintain terminal velocity declines- especially with lift from tail fins)

20000 meters: TWR = 1.72 (by this point, your should be burning at a rather significant angle relative to the vertical, in order to make your gravity turn)

25000 meters: TWR = 1.76 (gravity turn continues to deepen, but atmospheric drag is becoming much less of an issue)

30000 meters: TWR = 1.84 (atmosphere has become extremely thin, and rocket has reached a significant fraction of orbital velocity in the horizontal- assisting climb)

32000 meters: TWR = 1.96 (atmosphere continues to fall off, rocket continues to gain speed horizontally)

48000 meters: TWR = 2.04 (atmospheric drag is almost negligible, rocket should focus on achieving orbital velocity)

This is a rather low-resolution and approximate sketch of an ideal ascent profile, and HEAVILY affected by the size of the tail fins and any other aerodynamic surfaces relative to the rest of the rocket. It is backed by extensive experience from my own rocket launches, however.

All that being said, personally I prefer much higher TWR to reduce my play-time to orbit, a more important factor for me.

I've also been known to make use of much lower TWR to reflect the real-life balance between fuel cost and engine cost (engines are MUCH more expensive than fuel tanks and fuel, therefore it is usually preferable to launch with a lower TWR than aerodynamics would suggest- although real-life aerodynamics dictate entirely different ideal TWR than in KSP...)

Regards,

Northstar

Edited May 10, 2014 by Northstar1989

[Yasmy]

You're right. I started with (dW/dt)/F=(mgv+mva)/(mg+ma+kv2) = v / (1 + (k/(ma+mg)) v^2),

and normalized my definition of efficiency to be 1 at terminal velocity: e = 2 (dW/dt)/F /v_T.

I didn't realize that I had in the process assumed TWR of 2 when I changed v/(1 + (k/(ma+mg)) v²) to v/(1 + (v/v_T)²). That was sloppy.

So my analysis incorrectly only applied to flight at a TWR of 2, for which (ma+mg)/k = m|g|/k = v_T².

Instead (dW/dt)/F = v/(1 + (k/(ma+mg)) v^2) = v/(1 + (v/v_T)²/(TWR-1)).

Edited May 10, 2014 by Yasmy

[rkman]

Another factor KSP players typically forget in this discussion though- the ideal TWR is actually infinite...

Launchpad: TWR = 3

How much less delta-v does such a rocket need to get to lko than a rocket with a twr of say, 1.7?

[Yasmy]

How much less delta-v does such a rocket need to get to lko than a rocket with a twr of say, 1.7?

This is the whole point of this thread: Modest deviations from terminal velocity cost less than a percent delta-v to orbit. I.e.: It just shouldn't matter for most people.

If delta-v is what you care about, anything in the ballpark of terminal velocity has a tiny effect on delta-v to orbit.

Large deviations on the low end (starting TWR < 1.2-1.5) can cost a lot more in gravity drag (5-10% delta-v to orbit) but are more cost effective (engine count/cost/part number).

[Northstar1989]

How much less delta-v does such a rocket need to get to lko than a rocket with a twr of say, 1.7?

Maybe 100, 120 Delta-V at the most vs. a rocket with a TWR of 2 all the way up (achieved by lifting off with a TWR of 2 and then staging and throttling to keep it from rising higher)... No idea how that compares to a TWR of 1.7.

But remember, with a really large rocket, that sill represents a LOT of fuel and lost potential payload mass...

So not more than 3% Delta-V savings at a maximum.

I mostly use this knowledge as a guide for where to stage my disposable rockets- i.e. shortly before my gravity turn so that my TWR declines at this point...

Regards,

Northstar

Edited May 10, 2014 by Northstar1989

[Northstar1989]

Also, all of this assumes you're not playing with a revised aerodynamics module like FAR

If you're playing with FAR, and have a long, thin rocket with fairings; then your terminal velocity goes WAY up, and as a result the ideal TWR rises as well, since atmospheric drag is less of an issue, but gravity drag is still just as big a deal...

Regards,

Northstar

Edited May 10, 2014 by Northstar1989

[Alchemist]

Also, all of this assumes you're not playing with a revised aerodynamics module like FAR

If you're playing with FAR, and have a long, thin rocket with fairings; then you terminal velocity goes WAY up, and as a result the ideal TWR rises as well, since atmospheric drag is less of an issue, but gravity drag is still just as big a deal...

Keeping terminal velocity in lower atmosphere always requires TWR around 2, even with realistic aerodynamics. What changes is the terminal velocity itself. But with less drag you can benefit more from higher initial TWR , because it allows to reach the terminal velocity faster. On the other hand, this aerodynamics upgrade also makes it more beneficial to design long rockets (not wide) and they usually tend to have low launch TWR.

[Northstar1989]

Keeping terminal velocity in lower atmosphere always requires TWR around 2, even with realistic aerodynamics. What changes is the terminal velocity itself. But with less drag you can benefit more from higher initial TWR , because it allows to reach the terminal velocity faster. On the other hand, this aerodynamics upgrade also makes it more beneficial to design long rockets (not wide) and they usually tend to have low launch TWR.

In different words, isn't that what I just said?

I never said that the TWR necessary to keep terminal velocity goes up (although the time it takes to catch up to terminal velocity from stationary does- meaning that a higher launchpad TWR is desirable), only that the balance between atmospheric and gravity drag changes- making atmospheric drag relatively less of an issue, and making the fuel savings from reaching orbital velocity faster more important...

Regards,

Northstar

[rkman]

I'm not sure what you mean by "in the ballpark of terminal velocity". A launch twr of 3 would allow for a considerably larger part of the ascent to take place at terminal velocity than a twr of 1.7. Are you saying large deviations on the high end of launch twr is not worth it in terms of delta-v?