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Thinking about the no atmosphere caveat here made me think of Venus, which is the opposite of no atmosphere for solid/rocky bodies in our solar system.

Earth's low orbital velocity is about 7.8 km/s. It's common to tack on another 1 to 1.5 km/s for the gravity drag and to ignore atmospheric drag in comparison. It's true that modern vehicles often reduce thrust slightly near max-Q but it's not a huge effect.

But launching from the surface of venus with its 100 times higher atmospheric density and similar scale height poses a substantial penalty.

You could not accelerate at the same rate as Earth launches; you'd hit a brick wall from atmospheric drag, so you have to climb more slowly, and minimize the sum of the losses due to drag and gravity.

Is it possible to estimate how much larger these losses are on Venus compared to the roughly 1 km/s delta-v loss from Earth?

Has anyone already calculated how much slower you'd have to go at max-Q, or the number of extra minutes it would take to reach low Venus orbit (compared to Earth launch)?

uhoh
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    Surely no one would launch from the surface of Venus in a rocket, at least a chemically powered one. Surely you'd use a balloon of some kind to get to the upper atmosphere and launch from there? – Steve Linton Sep 27 '19 at 08:54
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    @SteveLinton I'm asking because I am serious. And don't call me Shirley – uhoh Sep 27 '19 at 10:39
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    @SteveLinton: I think it's a good question. The answer will support the notion that launching from Venus with a rocket is a bad idea. – DrSheldon Sep 27 '19 at 13:38
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    Funny, I was coming here to ask if this was even possible. Talk about timing. I think you should also consider the 500C difference in temperature – Diego Sánchez Sep 27 '19 at 13:58
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    The dv from surface to low Venus orbit has been estimated at 27000m/s by at least one “solar system subway map” but I don’t know how that was arrived at. I can try it in my sim over the weekend but I suspect it’s going to be very dependent on how much heating you can take. I’ll probably use a Q limiting approach as a proxy for heat limiting. – Russell Borogove Sep 27 '19 at 15:57
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    Can we launch from the Maxwell Montes? It'd take out a decent chunk of the pressure you would have to go through. From the graph I found if you started at 11km up you would cut out at least 20-30bar... not much of an improvement and youd still have the layers beyond the troposphere to deal with- no idea on that one. – Magic Octopus Urn Sep 28 '19 at 06:13
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    @MagicOctopusUrn: driving to the mountains before takeoff is a widely-known trick for shaving delta-V off of Eve ascents in Kerbal Space Program – Jacob Krall Sep 28 '19 at 13:42
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    You’d need rockets that were not over expanded at 90 bar so your isp is going to be pretty terrible, at least for the first stage – Steve Linton Oct 04 '19 at 10:57
  • @SteveLinton that's a really good point! Maybe it's time to consider reopening Could electric fans lift a rocket strait up like a multi propeller drone? – uhoh Oct 04 '19 at 12:28
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    "The rocket equation only accounts for the reaction force from the rocket engine; it does not include other forces that may act on a rocket, such as aerodynamic or gravitational forces. As such, when using it to calculate the propellant requirement for launch from (or powered descent to) a planet with an atmosphere, the effects of these forces must be included in the delta-V requirement" - Where, and how? How do you add a drag coefficient to the rocket equation? – Mazura Nov 06 '19 at 01:41
  • @Mazura I'm not sure how your comment applies to my question. It looks like you are asking a new question, so it should probably be posted as a new question, or on an answer that requires clarification. – uhoh Nov 06 '19 at 04:19
  • The question boils down to how to calculate delta-v without "[ignoring] atmospheric drag", no? – Mazura Nov 06 '19 at 04:24
  • @Mazura I see what you are saying now. Let's say on Earth using a nice rocket with a nice engine we can put 2% of the propellant's mass into orbit. A 100 ton rocket might be able to put 2 tons into LEO. We can still use the rocket equation to define that ratio in terms of a delta-v even though it's not equal to the final velocity. If the engine has an exhaust velocity of 3.5 km/s we can say that the delta-v of the launch is 3.5 ln(100/4) = 11.3 km/s, and if the orbital velocity is 7.8 km/s we can call the 3.5 km/s difference a delta-v penalty due to gravity and drag. – uhoh Nov 06 '19 at 10:28
  • @Mazura So a delta-v penalty can be a simple way to express the ratio of final to total mass in an approximate way. I'm not asking to use the rocket equation to calculate the launch, but the concept of delta-v can still be used to express the mass ratio in a convenient form. – uhoh Nov 06 '19 at 10:32
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    @RussellBorogove - were you able to complete your sim? – IronEagle Feb 21 '20 at 20:51
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    I'm gonna need the answer to a new question before I can make a realistic stab at this one. Stand by... – Russell Borogove Feb 22 '20 at 01:37
  • @RussellBorogove only 165 hours left! ;-) – uhoh Feb 22 '20 at 02:28

2 Answers2

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One could obtain an upper bound by reducing it in the following way:

  1. The mass density of the atmosphere is 65 kg/m³, which combined with a 15.9km scale height means that the atmosphere has roughly Earth density at 4 scale heights, or ~60km. Which means we can just use Earth number from there and out.
  2. We do a simple delta-v cost estimation for climbing up to 60km without much velocity gain. This is the "extra" part the Venus atmosphere is costing us.

This would not be the most efficient launch configuration, but it has the nice property that the "real" value is guaranteed to be less.

Furthermore, let's say that the ascent in 2) happens in 2 minutes at uniform velocity. Again, that's probably not optimal any way, but this is for an upper bound.

We need 500m/s from initial acceleration to climb in that time, but since we still have that velocity when we reach 60km whereas an Earth launch would start from 0 there, the naive assumption is to not count it as an extra cost.

2 minutes fighting Venus gravity is close to 1km/s, an extra cost for the way we are fighting the atmosphere. Tack it on to the usual "1 to 1.5 km/s" number, which now becomes "2 to 2.5 km/s".

For the drag equation, let's assume an extra stage on the bottom of the Saturn V. The aforementioned mass density, the 500m/s constant velocity, the drag coefficient, and an assumed 50% increase in cross section for the extra stage. This gives a force roughly equal to that of gravity at the beginning of the climb, but since the mass density quickly tappers off, it's going to be less than half than the gravity loss.

In conclusion, an upper bound is about 1.5 km/s more than a launch from Earth.

Here are some additional caveats.

  • Drag depends on the scale of the rocket, unlike most other factors governing delta-v. A very large rocket like the one-upped Saturn V imagined here suffers less from drag than a smaller rocket.
  • Engines will be less efficient in the thicker atmosphere. While this is part of the delta-v budget and not the cost, it still has large implication for a Venus launcher design.
SE - stop firing the good guys
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The answer is significantly dependent on how much aerodynamic pressure and heating you can tolerate, and whether it's possible to achieve high specific impulse from a rocket engine exhausting into Venusian atmosphere.

At 10km above the Venusian "reference altitude", a speed of only 46 m/s (~100 mph) puts you at a Q of 39.5kPa -- a little higher than "max Q" of most Earth-orbit launchers. If your Q limit is on that order of magnitude, it's going to take you a very long time to get out of the Searing Black Calm, which means you're going to lose a lot of delta-v to gravity -- it takes about 8 minutes going straight up before you can even think about pitching over into a gravity turn.

At least one person has estimated the delta-v to reach Venusian orbit at 27km/s, but they did not provide much detail on their methodology.

By having elfin engineers provide a magical rocket engine capable of ~240s specific impulse when exhausting into 60 atmospheres of pressure, I was able to reach orbit in my home-brewed simulation, lifting off from Maat (to save me 8km and 30 atmospheres of vertical suffering), with about 15000 m/s of delta-v. Max Q achieved was 55 kPa.

As an aside, I made a lot of fixes and improvements to my sim while trying to make it work for these extreme conditions.

If an answer to the question of specific impulse at extremely high exit plane pressure comes along, I'll take another pass at the simulation and give more detail. I suspect it will wind up closer to the 27km/s estimate than the 15km/s estimate.

Russell Borogove
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  • "magical rocket engine capable of ~240s specific impulse when exhausting into 60 atmospheres of pressure" That is a pretty big assumption, isn't it? Plus, could you run your sim from zero to see what it puts out? – Polygnome Feb 28 '20 at 22:37
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    Yes, it's a pretty big assumption (which part of "magical" was unclear?), and also obvious bait to provoke someone into answering the linked question. I'm not putting more work into this one without a sane engine spec. – Russell Borogove Feb 28 '20 at 23:47
  • I haven't given up on the Aerospike-SSME but it's pretty challenging to figure out the nozzle parameters. – Organic Marble Mar 01 '20 at 02:02