Why is it that Larger Rockets lose less delta v from drag?

[Spaced Out]

I just remember hearing that the Saturn V only lost around 40 m/s but some sounding rockets (sub orbital science roclets) lpse up to 1000 m/s. I just want to know why this is.

[p1t1o]

dV is not equivalent between different vessels.

Because in a large, heavy, rocket, 1m/s of dV equates to a large amount of kinetic energy, whereas in a small vessel, 1m/s dV requires a lot less.

Take two rockets, one small, one large, with the same amount of dV. The larger carries a lot more energy with it, which makes sense since a large rocket at 100m/s has/requires a lot more kinetic energy than small rocket at 100 m/s.

Probably the Saturn V lost a heck of a lot more kinetic energy than the sounding rocket, just to the sounding rocket that energy is worth more of its total dV.

Throw a rock at 10m/s, and ball of paper at 10m/s and which one has more energy? And which one slows down quicker? The rock probably loses more energy in total, but will slow down only slightly because you had to pump more energy into it to get it up to speed.

Edited September 6, 2017 by p1t1o

[kerbiloid]

Drag force ~ cross-section area ~ size².
Mass ~ volume ~ size³.

Drag acceleration = drag force / mass ~ size^-1

[Shpaget]

In addition to the previous replies, sounding rockets achieve, from the start of the flight, significantly higher accelerations meaning that they pick up a lot of speed early on in the thick parts of the atmosphere. Drag is a function of square of speed, so higher speeds bring a lot higher drag forces.

In contrast, Saturn V started off at around 1,2 G and never exceeded 4.28 (Apollo 7) and no more than 3,97 for the rest of the Apollo missions.

[Pand5461]

@Shpaget said probably the main reason.

Sounding rockets often have a few gees right from the launchpad, so they reach high speeds low above ground.

Also note that sounding rockets don't always have gimbaled motors (more often than not they have just simple solid rocket motors), so they need relatively large aerodynamic surfaces to maintain stability and those increase drag even more than 2/3rd power law.

Edited September 6, 2017 by Pand5461

[Laie]

@Pand5461: nay, do not underestimate the power of three.

Let's assume a ~500kg Sounding rocket, so the Saturn is a nice round 4096 times as heavy (16 times as tall and wide, 256x cross-section). The naive size calculation then tells me that a Saturn has 16 times as much heft per drag as the sounding rocket.

I'll leave it to someone else to figure out just how much extra drag you get from the speedy ascent -- from messing around in RO, I know that it's fierce, but I also know that you get out of it quickly. Whereas an orbital rocket tips over and keeps ploughing through a thin-but-still-substantial atmosphere at ever increasing speed. Max-Q may be lower, but the orbital rocket drags it out for much longer (no pun intended).

As for naiveté, I guess it matters that neither rocket is exactly pencil-shaped. The Saturn is more like a crayon, while the sounding rockets have the aspect of a knitting needle.

[Pand5461]

5 minutes ago, Laie said:

 

@Pand5461: nay, do not underestimate the power of three.

 

This is what I meant by 2/3rd power. I was thinking in terms of mass, so drag force scales as mass^2/3 if two rockets are perfectly similar. Acceleration scales as force / mass = mass^2/3 / mass = mass^-1/3.

What I also wanted to say is that it's probably even worse than mass^-1/3 in reality because most of sounding rockets have large (compared to their diameter) stabilization fins space rockets typically lack.

In your example, Sounding / Saturn deceleration ratio is probably even greater than 16.

However, I sincerely doubt that those 1000 m/s overwhelm reduced gravity losses with high-g launch.

[wumpus]

To a simple degree, the aero losses are inversely proportional to the height of the rocket.

Also your typical sounding rocket launches with a TWR often over 4 or 5, while Saturn launched at something like 1.15.  This means the sounding rocket had almost no gravity losses  while the Saturn threw away 5 kg of fuel/oxidizer fighting gravity for every 1kg used for delta-v (at least until a significant amount of stage 1 was burned up and TWR rose above 2).  So next to no gravity losses has to be compared to the disadvantages of going through the atmosphere at such a high speed.  Finally, I suspect that you get some sort of Oberth effect in really hitting your engines while still in the atmosphere, although I suspect it is entirely eaten up by drag losses.

So optimal TWR is complicated.  And what works for sounding rockets doesn't always work for orbital and beyond.  You would think that you could compute ideal TWR via sounding rockets (for KSP, for example), but it turns out that the values change as you pitch over.  So in KSP expect to need mechjeb to either fly the same route every time or recompute an ideal curve based on TWR.  Mechjeb wasn't up that that (nor was I ready to hack mechjeb to do it) when I was trying to figure out optimal TWR (I still don't know it, but think you should launch a bit below 2.0).

[Pand5461]

9 hours ago, wumpus said:

You would think that you could compute ideal TWR via sounding rockets (for KSP, for example), but it turns out that the values change as you pitch over. 

Actually, there is also something here that KSP does not model properly.

Higher TWR is always more efficient (given that you can restart engines, so you can include coasting phases between burns) in terms of delta-V for a given rocket design. But there is a huge BUT here: for a given rocket design. Rocket structure must withstand engine thrust, so increasing TWR means you need a stronger rocket, fairings, payload adapter and payload itself, meaning you need to include more "dead" weight. And you will need heavier engines of course and a way to ensure they can restart in flight. So a weaker but lighter rocket might actually deliver a heavier payload, despite losing more delta-V on gravity.

[wumpus]

5 hours ago, Pand5461 said:

Actually, there is also something here that KSP does not model properly.

Higher TWR is always more efficient (given that you can restart engines, so you can include coasting phases between burns) in terms of delta-V for a given rocket design. But there is a huge BUT here: for a given rocket design. Rocket structure must withstand engine thrust, so increasing TWR means you need a stronger rocket, fairings, payload adapter and payload itself, meaning you need to include more "dead" weight. And you will need heavier engines of course and a way to ensure they can restart in flight. So a weaker but lighter rocket might actually deliver a heavier payload, despite losing more delta-V on gravity.

That seems a bit questionable.  I rather doubt it is true for Eve (or Venus) and that if it is true on Kerbin (and Earth) that there should exist some TWR that has higher aero losses than an ideal TWR.

Cannon to orbit would be the extreme example, a projectile screaming through the atmosphere at mach 20 (or more, should you be trying for escape velocity or solar escape velocity) should have more aero losses than the combined aero and gravity losses of a rocket with TWR between 5-10.  Obviously on airless planets increasing TWR is strictly more efficient, but including an atmosphere adds a variable that has to be considered.

That said, in KSP you should almost never reduce your SRB thrust (stability and control being the reasons for nearly all exceptions), and often it makes sense to keep your liquid rockets at full blast[during ascent] even though the rocket equation tells you to use them later for more delta-v (assuming you also have SRBs with lower Isp running at the same time).  This challenge:

(there was a later 1.1.3 challenge as well) implied that launches with a TWR of 2.0 was most efficient to LKO and that adding more "kickers" (the largest SRB and inevitably the first stage in this challenge) didn't make for a more efficient rocket (even though a "kicker" was an efficient means of adding delta-v as well as TWR).  If you hear a kerbanaut insisting that TWR of ~1.2 is "most efficient", that probably came from using exclusively liquid rockets (where fuel tanks are cheaper than higher thrust engines).

That said, I'd be curious how such a challenge would play out using a mod that gave SRBs the same Isp as mainsails or skippers.  I wouldn't at all be surprised if they used a launch TWR of 5-10 and were limited by things like maxQ and control (launch at a steep angle).  I just don't think that "cannon launch" will be as efficient (and remember, there have been some work on cannon-based space launches on Earth.  It isn't  strictly theoretical).

[Pand5461]

2 hours ago, wumpus said:

Cannon to orbit would be the extreme example, a projectile screaming through the atmosphere at mach 20 (or more, should you be trying for escape velocity or solar escape velocity) should have more aero losses than the combined aero and gravity losses of a rocket with TWR between 5-10. 

I did not make myself absolutely clear with "given that you can restart engines" thing. The extreme example I had in mind is the engine that can switch between "full steam ahead" and "stop thrusting" infinitely fast, which gives it, in essence, any TWR needed. So (surprise!) the rocket which always has the most optimal TWR is the most optimal.

This is not even remotely realistic, of course.

And I don't think TWR of 5-10 on solid motors will be much better than 2. The reason for not improving after TWR=2 is, I guess, because this is just shifting maxQ region closer to ground and prolonging its duration.

The Goddard's problem solution for vertical ascent is that most fuel-efficient way to get straight up is to keep drag force equal to gravity. In case of constant-density atmosphere, this transforms to "get to the velocity when drag=gravity as soon as possible, then keep TWR=2", therefore that magic number.

[magnemoe]

13 hours ago, Pand5461 said:

Actually, there is also something here that KSP does not model properly.

Higher TWR is always more efficient (given that you can restart engines, so you can include coasting phases between burns) in terms of delta-V for a given rocket design. But there is a huge BUT here: for a given rocket design. Rocket structure must withstand engine thrust, so increasing TWR means you need a stronger rocket, fairings, payload adapter and payload itself, meaning you need to include more "dead" weight. And you will need heavier engines of course and a way to ensure they can restart in flight. So a weaker but lighter rocket might actually deliver a heavier payload, despite losing more delta-V on gravity.

Engines are expensive, adding some meter of tank is cheap, this is why the saturn 5 and many other large rockets has low initial twr. 
Secondary, sounding rockets are often based on adding an extra stage to older surface to air missiles or using an derivative of this designs, this give high twr. 
Know Nike ajax was standard for an long time in Norway and we use lots of sounding rockets to study polar light. 

[sevenperforce]

Large rockets have a higher cross-sectional density than small rockets for a given fineness ratio. That's just geometry.

[Bill Phil]

Volume, and thus density, and thus mass, and thus energy, scales with the cube, whereas the area, which determines drag, scales with the square, less if we're talking about cross-sectional area. A larger increase in available energy and a not so large increase in drag (for a given flight profile) means that a larger rocket is more efficient.