How do I calculate Delta-V INCLUDING DRAG

[Cheif Operations Director]

I would like to calculate the Delta-V of rockets including drag. I looked it but but I couldn't get a straight answer,

 

Any ideas?

[Bill Phil]

Air drag is usually a very small loss, while gravity drag is far worse. 

Air drag is a function of air density, velocity, reference area, and coefficient of drag. Two of those depend on the rocket's shape, and one is a function of time and the other a function of altitude. It can be done, and is, but there are a lot of variables involved. Just give yourself a good margin.

[sevenperforce]

Air drag is almost always determined by wind tunnel testing; it's far too complex to be done reliably any other way.

[wumpus]

2 hours ago, sevenperforce said:

Air drag is almost always determined by wind tunnel testing; it's far too complex to be done reliably any other way.

In KSP your best bet is to go into the "cheat menu" and turn off gravity.  Take your vehicle and launch it perfectly horizontally (the spaceplane hanger will do wonders, although you might need launch clamps to keep it off the runway), and see how long it takes to slow down, this should at least give you indications of air resistance at that speed regime and altitude (subsonic, transonic, and supersonic should behave differently, although it might require Ferum to get this right).

Notes from NASA: https://spaceflightsystems.grc.nasa.gov/education/rocket/flteqs.html

More: https://www.grc.nasa.gov/WWW/K-12/airplane/dragco.html

(I deleted a more ground-biased example that I wrote.  Stick to NASA's explanation).

Also, your gravity losses are relatively easy: (TWR-1)/TWR.   If you are doing a relatively natural "gravity turn", you should be able to substitute (cos(angle of attack)(TWR-1))/TWR.  But now you have a nasty calculus problem that requires you to also already know the path you are taking, not to mention the complexity of the aero-fixed equation.  Don't expect to be able to be able to come up with a "God equation" that lets you specify an ideal rocket.

 

[winged]

On 16.04.2018 at 8:52 PM, wumpus said:

In KSP your best bet is to go into the "cheat menu" and turn off gravity.

You can also use MJ which will show you delta V losses due to drag and gravity, like on the picture below:

 

[Mark Kerbin]

Get Kerbal Engineer Redux. 

Thats your only good option for getting DV easily. 

[Crown]

On Montag, 16. April 2018 at 12:17 AM, Cheif Operations Director said:

I would like to calculate the Delta-V of rockets including drag.

Hi,

as far as my knowledge goes, delta-v is not calculated with drag. Only without drag.

The reason for this might because drag is highly depended on the flight profile (pressure, speed, rocket shape, ...). For Kerbin, there is a delta-v map (search for "Kerbin delta-v map" if you want it) which shows the delta-v needed for inter-planetary travel, incl. landing and ascent. The delta-v needed for LKO, for example, includes drag. For my rockets, I take a few hundred more because I know that my ascent path is far from ideal.

If you want to know what your rocket's delta-v is, there are several ways. One would be to download a plug-in for KSP to just display it. Kerbal Engineer Redux, as mentioned above, is one option. I use VOID ("Vessel Orbital Information Display") which uses KER as well but also shows several other information about the rocket.

ou can calculate the rocket's delta-v by hand, too, if you want. The which is the Tsiolkovsky rocket equation

is all you need.
Everything needed is written in the article, so I want to redirect you there.

If your question isn't answered yet, don't hesitate to write some more lines to clarify ;-)

[virchau]

As others have mentioned in the thread, air drag is of little to no importance - past the sound barrier, most of the drag disappears. KER and MechJeb don't do drag calculations like that for you anyway, since it's basically impractical and mostly useless to calculate. However, the reason why rockets have less dV in atmosphere is because of the reduced Isp (efficiency.)

If you go to the VAB and mouse over the engines, you should see that they have a 'Sea-level Isp' listed somewhere. This is exactly the kind of thing that is required.

This is the dV equation:

To calculate the dV of a rocket starting from sea level, simply swap out the specific impulse in vacuum with the sea-level specific impulse.

[Cheif Operations Director]

Thank you everyone for the help. I'm not using this for KSP but real rocketry so I unfortunately don't have said tools. How do I calculate gravity drag then.

[YNM]

13 minutes ago, Cheif Operations Director said:

How do I calculate gravity drag then.

Gravity drag is the "amount" of "dV" you spent fighting gravity (going vertical/radial) rather than orbiting (going... "horizontal" ?).

As you might see, it depends on the rocket and trajectory (path and attitude) used.

[Cheif Operations Director]

On 4/26/2018 at 11:29 PM, YNM said:

Gravity drag is the "amount" of "dV" you spent fighting gravity (going vertical/radial) rather than orbiting (going... "horizontal" ?).

As you might see, it depends on the rocket and trajectory (path and attitude) used.

Exactly so how do I calculate it. Of course I know I'll need variables 

[Bill Phil]

8 minutes ago, Cheif Operations Director said:

Exactly so how do I calculate it. Of course I know I'll need variables 

https://en.m.wikipedia.org/wiki/Gravity_drag

You can find your average angle of attack over a rocket launch and multiply gt by the sine of that angle and you get a decent approximation.

[Cunjo Carl]

Ah, this is an interesting one, I've never really thought of expressing launch losses in terms of deltaV directly, though it makes a lot of sense now that you mention it. If you want to do it yourself from theory there's a few good answers, depending on the context. I'm going to start from the easiest, and move towards the 'best'. In practice, I do the the easy street technique along with trial and error rocket design, but it's nice to see what we could do if we wanted to spend more time with a calculator.  There's a slight rephrasing of your question that works nicely:

Q: What percentage of my rocket's deltaV was useful for increasing my rocket's energy?

Here's an example. For now, we're working backwards from what you probably want, but we'll get there. Let's say I have a rocket that used 3400m/s to get from KSC (planet turning at 175m/s) up to LKO (2300m/s, 70km). Also, as a note, all of these formula can be used in real life or KSP for transfers between orbits as well as launches/landings.

With some assumptions (uniform gravity = useful for trips to suborbit or low orbit) the formula boils down to

(sqrt(v_final^2 + 2*g₀*Δaltitude)-v_initial)/ΔVused
(sqrt(2300^2 + 2*9.8*70000)-175)/3400
So.... 70% of our deltaV was useful. This would be pretty typical for Kerbin launches, and much of the losses occur due to gravity in the first moments trying to pry yourself off the launch pad.

If we take away the uniform gravity assumption, it becomes:

[ sqrt(v_final² - 2* μ_planet*(1/r_final - 1/r_initial)) - v_initial ] / ΔVused
[ sqrt(2300^2-2*(3.5*10^12)*(1/670000-1/600000)) - 175)] / 3400
...  which equals a slightly differenter 70%. Note, μ is the standard gravitational parameter for your planet.

Q: What percentage of my rocket's used deltaV was necessary to get to my orbit?

One notable downside of the previous energy based system is that it's physically impossible make a 100% efficient rocket in those scales. So, we can make a system where 100% is rescaled to be the best achievable efficiency with a touch of added difficulty:
Working on the assumption that Houghman is the best transfer for us (typically it either is, or is quite close), we can find how efficient our rocket is compared to the best ideal rocket. As a note, for going to orbit from the ground, the answer is not very different.

( sqrt( μ_planet)*[ sqrt(2/(r_final+r_initial)) * (sqrt(r_final/r_initial)-sqrt(r_initial/r_final)) + sqrt(1/r_final) ] - v_initial )/ΔVused
( sqrt(3.5*10^12)*[ sqrt(2/(670000+600000)) * (sqrt(670000/600000)-sqrt(600000/670000)) + sqrt(1/670000) ] - 175 )/3400
...Which is an even slightly differenter still 70%!

Q: Can we predict what percentage of a hypothetical rocket's deltaV will be useful for increasing it's energy?

   Yes! (with a lot of effort) . As a disclaimer, I've never used this one in practice, so I'm only 90% certain I've got it right. I just ran the derivation this afternoon, and I'm still getting my physics sea-legs back from a bit of a break, so maybe I should say more like 80% certain.... It sure looks right! It acts right in its limits. Here the contents of the cosine represent the difference in angle between your velocity and where your rocket is pointing. On the launch pad, it's 90 degrees, which makes your deltaV efficiency pretty abisimal off the launch pad. Incidentally, you can choose your vstart to be whatever you want, including 0. You just need to keep your frame of reference consistent.
   
   { sqrt[ TimeIntegral( v*(g₀*TWR*cos(phi_Heading-phi_Trajectory) - F_aerodrag)*dt) + v_initial^2 ] - v_initial }/ΔVused

This could be coupled with techniques for determining trajectories to orbit, and rocket TWR/ISP efficiency charts to make some useful predictions. It would wind up requiring atleast a spreadsheet solver in any case though.

Oh, and if something in here didn't help, let me know more what you have in mind, and I can try to drum up something more specific. Also, let me know if you'd like the background/derivation for any of the formulas. Well, I hope something in there helps! Have fun.

Edited May 3, 2018 by Cunjo Carl