# Specific impulse and delta-v in Tsiolkovsky's rocket equation

According to Tsiolkovsky's rocket equation, it is possible to calculate the delta-v of a multistage rocket if you know the characteristics of each stage of the rocket. In my case, the only characteristics that I have found on a rocket's data-sheet/catalog were the following: vacuum specific impulse, initial and final masses of each stage of the rocket.

My questions are:

• A rocket has a vacuum and a sea-level specific impulse. Which one of these two should I use to calculate the total delta-v of a multistage rocket?
• Tsiolkovsky's rocket equation is applicable for a rocket which is not subject to external forces. How do I "correct" the delta-v for lower-stage rockets? What are the delta-v losses that should be accounted for?

• It depends how accurate you want to make the calculation and how much information you can find concerning the rocket. Some other points to consider in addition to air pressure differences on engine performance are: the aerodynamics of the rocket itself and air resistance changes with altitude, the latitude and altitude of the launch site, the direction of the launch, gravity losses and down throttling, both to avoid dynamic stress at Qmax and later to avoid excessive g forces. But it’s not rocket science… no wait… Apr 1 at 18:19

The rocket equation is meant to work with constant specific impulse. If you want to stay with the Rocket Equation, you can 'split' any stage into more 'virtual' stages (where the initial mass of the next stage is equal arbitrarily chosen dry mass of the previous one), find what delta-V you need to reach roughly 10km altitude and generate a 'virtual' stage accordingly, applying sea level ISp for that part, then vacuum for the remaining stages. If you want a more precise result, you'll split the stages into infinitely many parts using calculus, and integrate with variable specific impulse changing with the atmospheric pressure.

As for external forces - you first calculate the delta-V as if they didn't exist, and then add the losses they cause to your required budget: to reach Earth LEO you need over 9km/s of delta-V even though you only reach around 8km/s of velocity, the extra 1km/s is swallowed by atmospheric and gravity losses.

• Would it be wrong to use the vacuum specific impulse (ivac) for lower stages and then add the drag and gravity losses after calculating the delta-v? The reason I ask this is because, for example, reading Vega's user manual, the only information I found were the ivac for all stages. Here's the link to the manual. Apr 1 at 13:04
• @Miguel Specific impulse loss (due to lower pressure differential between combustion chamber and the outside) is separate from drag and gravity losses. The one problem with using vacuum ISp early on is that fuel usage (and so, mass change) is largest early on, so pretty small errors early on can drastically change the delta-v. It's a short segment of flight but very impactful.
– SF.
Apr 1 at 13:22

What you're asking here is how to take into account waste variables such as gravity loss, aero-forces, and ISP loss at sea level. These all depend on your rocket's specific flight profile. For example, rockets with high thrust to weight ratios will experience less loss due to gravity, but much greater loss due to air resistance. Your thrust to weight ratio also governs how much time you spend in the lower atmosphere, which changes the average specific impulse over the duration of your flight.

Here's the scoop:
Delta V can be very useful for deep space orbital calculations, but when dealing with ascent to orbit it's not super helpful. If all you have are delta V numbers though, you can make a rough guess that you can achieve low orbit with <10 km/s of fuel.

Hope this helps!