Ditch empty stages while coasting?

[A_name]

During launch, ignoring drag, does keeping an empty stage while coasting to apoapsis cost me velocity? My intuition says the heavier I am the more gravity losses I'll suffer. But it also tells me that if I already have the energy to loft myself to x altitude I already paid for those gravity losses. So which is it? 

[Garrett Kerman]

With KSP physics, keeping the stage will cost you no more than if you detached them. The only time it would matter is when you're burning to make orbit. That extra mass makes your spacecraft less efficent.

[hawkinator]

It's the second one. While your coasting, removing parts from the rocket doesn't change the vehicles trajectory (except for slight bumps from the decouplers and the like). So if your coasting to an apoapsis of, lets say, 150 km, then you'll get to 150 km whether you keep that empty stage on or not. Similarly, if you detach from the empty stage (in vacuum), then you'll notice it will follow you up to the apoapsis. 

BUT:

If you're still in the atmosphere, then it can make a difference. That empty stage can add extra drag. At some point in the upper atmosphere, this effect becomes negligible, but it's something to be aware of for a few cases. Your question says to ignore drag, so I'll assume that this question comes up for you around the 60+ km mark, where you start to not really worry about air very much during launches.

That said, while your not really losing much by holding on to empty stages during the coasting to apoapsis phase, there's not really anything to gain that way either, since you'll probably just need to ditch the empty stage once you get to the circulization burn anyway.

[Aegolius13]

I think you're better off keeping it, as least as it's not much wider or draggier than your upper stage.  

19 minutes ago, A_name said:

My intuition says the heavier I am the more gravity losses I'll suffer. But it also tells me that if I already have the energy to loft myself to x altitude I already paid for those gravity losses. So which is it? 

Putting aside aerodynamics for a minute, the second one.  The lighter ship is less affected by gravity, but also has less total upward momentum (or kinetic energy), so it balances out.  Kind of the reverse of the fact that objects fall at the same rate, regardless of mass.  So in a vacuum, it makes no difference.  

Now, putting aerodynamics back in: a long 2.5 m rocket including a spent stage has more total momentum than a short 2.5m rocket without the extra stage (since it's a larger mass travelling at the same speed).  But the longer rocket probably undergoes only a little more drag (assuming you have a streamlined profile).  So I believe the bigger rocket will incur a smaller velocity loss due to drag.  The exception might be if the spent stage is much draggier than the top one (wider body, lots of radially attached junk, etc.).

[Kerbart]

1 minute ago, hawkinator said:

If you're still in the atmosphere, then it can make a difference. That empty stage can add extra drag. At some point in the upper atmosphere, this effect becomes negligible, but it's something to be aware of for a few cases.

That depends largely on your design; it can very well go the other way. My rockets tend to have a Titan/Delta-like design with a central core that (after ditching the side-boosters fairly early in flight) doesn't change that much in diameter, hence it doesn't reduce resistance that much when I drop the bottom stage.

But... it does reduce mass by a significant amount. And with F = m×a the deceleration as a result of drag will be a lot more when I cut mass in half or more, while air resistance stays the same.

If the bottom stage adds a lot of resistance it's a different story of course. But that all depends on the design.

[Blaarkies]

Short answer: No

Long answer: Noooo!

Just kidding
Remember Galileo and the Feather and the Cannon ball? Imagine a feather in orbit(70km?) and a cannon ball beside it. Both will orbit equally efficiently no matter the mass.

Now imagine the Cannon ball in an orbit of 65km: it might be able to do an entire orbit before hitting the ground. Let's remove the cannon ball's contents(so that it becomes a thin shell, with a mass of just a few grams). Now it will only complete a half orbit, since it is more "feather-like".

My point: If your stage makes the craft more "cannon-ball-like", keep it. That momentum and gravity losses are already paid for(as you mentioned), thus making the craft more "feather-like" is worse for you. Mostly this comes down to a fairing making the craft more aerodynamic(less aero drag per more mass = cannon-ball-like), so keep them fairings and pop them just before your next upper-atmosphere burn.

Keeping a massive booster stage connected...well it depends. If it is aerodynamic(minimal fins) you might as well keep it. To make it clear, test these thing out. Get yourself into a sub-orbital trajectory, jettison the booster stage, but don't continue your burn. If the booster stage goes ahead of your craft, then it is more cannon-ball-like and you should keep it

* "Galileo and the Feather and the Cannon ball" is made up and not real.

[Spricigo]

W=m*g

F=m*a

If F=W then a=g

[A_name]

Thanks everyone for your so helpful answers. I am usually inclined to keep the spent first stage until I'm in the really high atmosphere where I can be sure my second stage won't flip upon decoupling! (thank you ksp aero :)) I worried I was somehow losing velocity to gravity by keeping it, but it's all clear now. Thanks again. 

[Superfluous J]

3 hours ago, A_name said:

really high atmosphere

 

I know you said to ignore air drag, but it does actually exist and keeping side tanks - even aerodynamic ones - will introduce drag that will slow you down. You're better off designing your craft to be able to drop them when empty.

[Kryxal]

Side tanks would, due to the clear increase in cross-section, but anything in-line would be worth keeping until you need the next stage cleared to burn.  Those would increase mass more than drag so long as you don't turn off prograde.