# What is the delta-v range for model rockets?

I'm curious about the delta-v of model rockets. While searching the web I found NASA's "For Educators" page How Do Rockets Stack Up that was going to cover it, however the stats haven't been filled in.

• "This is where the stats will go. The stats will go here." Oof. NASA's falling behind. – HDE 226868 Oct 23 '14 at 0:20
• What would you define as a "model rocket"? And why are you interested in the delta-v? I don't think that's a very informative parameter in non-orbital applications. – Rikki-Tikki-Tavi Oct 23 '14 at 0:42
• Anything from here would be considered a model rocket I guess. I'm interested in what the delta-v would be for pure curiosity. It struck me as odd that there were no clear answers on google so I though I'd ask. – Ceribia Oct 23 '14 at 1:30

It's common for the sort of model rocket you link (e.g. Estes kit with a D-class motor) to go to approximately 1000 ft altitude. If we assume an impulsive burn (reasonable, given that burn time << flight time) we can calculate the corresponding delta V with high school kinematics:

$$v^2 = u^2 + 2as$$

v = final velocity = $0$ (at apogee)

u = initial velocity (to be solved)

a = acceleration due to gravity = -9.8 m/s$^2$

s = distance traveled = 1000 ft ~= 300 m

solving, $$u = \sqrt{2 \cdot 9.8 \cdot 300} = 77 \space m/s$$

• Well, this neglects air drag, but I guess it works if you just want a rough estimate. – Rikki-Tikki-Tavi Oct 23 '14 at 11:04
• Isn't air drag accounted for with the approximate 1000 ft altitude? – Scott Oct 23 '14 at 19:42
• It does indeed neglect air drag. You could take another approach and look at the motor thrust profile, integrate that to determine total impulse and an effective specific impulse, plug that into the rocket equation along with the full and empty mass of the rocket. But that requires several more pieces of information that one would have to determine for a particular rocket. I took the approach in my answer for simplicity, because it only needs one input (the apogee height). – pericynthion Oct 23 '14 at 19:58
• It's also possible to use the published ISP of Estes' rocket motors (which are all black powder + oxidizer) to compute the delta-v. The specific impulses range from about 80 to about 90 for Estes motors. There's a handy "I'm too lazy to do it myself" delta-v calculator at strout.net/info/science/delta-v It also ignores drag. Given some very rough guestimates of ending weight vs starting weight, I get ~ 140 m/s delta-v. – Kirkaiya Oct 23 '14 at 20:14
• Since it's just for curiosity ignoring drag and making a wide estimate seems reasonable. 77-140m/s will work just fine. – Ceribia Oct 23 '14 at 20:59