Launch to orbit delta-v penalty from Venus compared to Earth?

Question

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)?

Answer 1

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.

Answer 2

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.