Calculating CD from Logged Data

[gdjsky01]

Back in the day, Konrad Hambrick (sp?) showed me way to calculate the approximate CD of a rocket using the data from a Black Sky AltAcc 1a/2. That was many many many many moons ago, and I am afraid I have no idea anymore how it was done.


I have a PNut, a Stratologger, and an Altimeter Two (as well as my old AltAcc). Is there a way to work out the rough CD of a rocket from the data logged?

Now I am no math genuis, so try and make any advice, "CD calcs for a dummy." :bangpan::bangpan::bangpan: :blush::blush:

 

[Handeman]

I would also like to hear how this is done, but I suspect it isn't that simple. Rockets have a Cd profile. The Cd changes with speed. Look at the Aerolab profile files sometime.

 

[gdjsky01]

I would also like to hear how this is done, but I suspect it isn't that simple. Rockets have a Cd profile. The Cd changes with speed. Look at the Aerolab profile files sometime.

I understand. I am looking for a rough idea. If not possible, not possible. I'll move on.

 

[jsdemar]

The best way to find the drag coefficient is to look at the deceleration during the coasting phase after motor burnout. The mass is not changing and you don't have the variability of the motor thrust curve. Assuming a vertical flight, you have two forces: Weight = m*g (mass times acc of gravity) and Drag force (Fd = 1/2 * rho * v^2 * Cd * A), where rho is air density (1.29 kg/m^3 at sea level), and A is the cross-sectional area (in m^2).

From the deceleration curve, find Fd = m*(a-g). Where m is rocket's mass minus mass of propellant. Convert mass to kg, convert a to m/s^2. Use g=9.8 m/sec^2. You will have a time-varying curve for drag force in Newtons (which are kg*m/s^2).

Now generate a velocity curve. If it's an acc-based altimeter, integrate the acceleration curve. If it's a pressure-based altimeter, differentiate the altitude curve for velocity (noisy!) and differentiate again for acceleration (very noisy!!). Scale the velocity curve to m/s. From the velocity curve and the drag force curve above, calculate the drag coefficient as a function of velocity:
Cd = 2* Fd / (rho * v^2 * A)
Substituting Fd from above:
Cd = 2* m*(a-g) / (rho * v^2 * A)
note that 'a' and 'v' are both from time-aligned curves.

As you can see, it's better to use an accelerometer-based altimeter to extract Cd. 'v' is derived from 'a' by integration (area under the curve).

 

[Zephhyr]

I knew those Calculus classes would be good for something someday:eyeroll:

The best way to find the drag coefficient is to look at the deceleration during the coasting phase after motor burnout. The mass is not changing and you don't have the variability of the motor thrust curve. Assuming a vertical flight, you have two forces: Weight = m*g (mass times acc of gravity) and Drag force (Fd = 1/2 * rho * v^2 * Cd * A), where rho is air density (1.29 kg/m^3 at sea level), and A is the cross-sectional area (in m^2).

From the deceleration curve, find Fd = m*(a-g). Where m is rocket's mass minus mass of propellant. Convert mass to kg, convert a to m/s^2. Use g=9.8 m/sec^2. You will have a time-varying curve for drag force in Newtons (which are kg*m/s^2).

Now generate a velocity curve. If it's an acc-based altimeter, integrate the acceleration curve. If it's a pressure-based altimeter, differentiate the altitude curve for velocity (noisy!) and differentiate again for acceleration (very noisy!!). Scale the velocity curve to m/s. From the velocity curve and the drag force curve above, calculate the drag coefficient as a function of velocity:
Cd = 2* Fd / (rho * v^2 * A)
Substituting Fd from above:
Cd = 2* m*(a-g) / (rho * v^2 * A)
note that 'a' and 'v' are both from time-aligned curves.

As you can see, it's better to use an accelerometer-based altimeter to extract Cd. 'v' is derived from 'a' by integration (area under the curve).

 

[1tree]

You might want to look at this:
https://www.apogeerockets.com/education/downloads/Newsletter303.pdf