Calculation discrepancy in delta v

[xlm]

We probably all have seen the community delta v map. It says that to achieve low kerbin orbit you would need 3400 in delta v. So I tried to calculate that by hand, here's how: the increase in potential energy equals mgh (I'm assuming constant g, in fact it would be even lower). The increase in kinetic energy is 0.5*mv^2. Assuming we are trying to achieve low orbit at 75km, the total delta v (calculated by sqrt(2*E/m)) would be about 2850m/s, and I didn't even use the rotation of kerbin itself.

In reality I was able to send rockets in low orbit with slightly less than 3400, but still way more than 2850. Granted that I didn't consider aerodynamic forces but how much could that be? So what am I missing? (And if it is air resistance, I'd appreciate if you could provide some calculation on that)

[bewing]

You have to include the gravity losses for the time it takes to reach a significant fraction of orbital velocity.

 

[GoSlash27]

xlm,

It's the atmosphere that makes it impossible to calculate precisely. For an airless body the process is much more straightforward: Calculate Vorb at sea level, add the DV to transfer to desired orbital altitude, and subtract the planet's rotational velocity.

For an airless Kerbin, sea level Vorb is 2,426 m/sec. Hohmann transfer to 70km is another 130 m/sec. Kerbin's rotation is 175 m/sec. So theoretically the minimum DV is 2,381 m/sec. But you have to follow a gravity turn to keep out of the denser part of the atmosphere, you have gravity losses and drag losses. All this together makes 3,400 m/sec about normal for a launch.

Best,
-Slashy

[Kryxal]

Gravity losses are bigger than they might otherwise be because the general rule is to start with a lower TWR (engines cost, fuel and boosters not so much).  Gravity losses are also increased because aerodynamic forces won't let you execute a low-altitude takeoff as you might on the Mun.  Not only would drag be too high, but a rocket not facing into prograde is just asking for trouble...

Edited January 16, 2018 by Kryxal

[Spricigo]

 

As pointed out you need to consider your losses: gravity, drag, cosine.

That means that for a precise calculation you need to consider all the forces acting in the vessel (thrust, drag, weight), and integrate it. The fact that we are talking about vectors add the complication that we need to consider the direction of those forces also. Drag is pretty difficult to consider since it depends on the density of the atmosphere, velocity and AoA of the vessel. But IMHO its the cosine loses that are impossible to predict,(seriously, it's affected by the amount of coffee that you drink)

[foamyesque]

The real killer is the gravity losses that the atmosphere necessitates. Drag losses themselves are reasonably small on an efficient ascent, especially with larger/lower-TWR rockets, but keeping them small and/or avoiding thermal implosion means you need to do a lot more climbing than otherwise, while avoiding sharp turns and staying prograde-- so you end up thrusting against gravity for a much longer period than you would otherwise.

Edited January 16, 2018 by foamyesque