Cool that our numbers agree, thanks for supplying them! Though I'm not sure I follow your math? The nose cone section decelerates for two reasons: (1) drag on the nose cone and (2) shear pins/friction holding it to the booster. Your math seems to be assuming that only (2) applies. To see why this matters, imagine the nose cone had massive massive drag (like a forward facing sphere or something). The rocket would decelerate quickly, but would obviously not try and separate. For this absurd rocket though, your math would take that high G decceleration, multiply by the weight of the nose cone, and assume that there was a strong separation force.
Instead, I manually worked out an equation that I've seen online as well (math is too long to post here) by calculating the force of drag on the nose cone, force of drag on the booster, and then finding what force the shear pins much exert such that the booster and nose cone decelerate at the same rate. If M is the mass of the rocket, mb is the mass of the booster section, a is the (open-rocket sourced) deceleration of the rocket at burnout, and R is the ratio of the Coefficient of Drag for the nose cone divided by Cd for the booster, then the force exerted on the shear pins (positive means the rocket tries to separate) is:
Fsep = a * (M/(1+R) - mb)
One other thing - your Cd numbers are far far lower than what openrocket has for me. If I set to "smooth paint", I'm at 1.1 at Mach 1, and have Cd of 0.88 according to component analysis. This is concerning.... I get Cd numbers like mine if I use the .rkt file from madcow.... Did you build your openrocket model from scratch or start from something you found online?
I'm enjoying this in-depth discussion.
I agree with what you say for (1) plus (2). I was being conservative.. but failed to state that. I made the conservative assumption that the drag force from the booster, booster base drag and fins >> drag force from the nosecone and payload tube. (I'm at work and feel a bit compressed on the rare day I reply to a forum post) This assumption seems to jive with your equation by setting the value of R to 0. I did look at the component drags in Open Rocket and at around Mach 1.14 or so, the Cd was at it's maximum value around 0.67. Let me post the actual numbers I have (I wish I were at home as I could just upload a screen capture instead of typing all this):
Burnout Mach Number = 1.14
Drag Components at Mach = 1.14:
Nosecone_____: Pressure Cd = 0.03, Base Cd = 0.00, Friction Cd = 0.03, Total Cd = 0.06
Payload Tube_: Pressure Cd = 0.00, Base Cd = 0.00, Friction Cd = 0.04, Total Cd = 0.04
Alt Vent Ring: Pressure Cd = 0.00, Base Cd = 0.00, Friction Cd = 0.00, Total Cd = 0.00
Booster Tube_: Pressure Cd = 0.00, Base Cd = 0.22, Friction Cd = 0.09, Total Cd = 0.31
Forward Fins_: Pressure Cd = 0.06, Base Cd = 0.00, Friction Cd = 0.03, Total Cd = 0.09
Aft Fins_____: Pressure Cd = 0.14, Base Cd = 0.00, Friction Cd = 0.02, Total Cd = 0.16
TOTALS_______: Pressure Cd = 0.24, Base Cd = 0.22, Friction Cd = 0.21, Total Cd = 0.67
Given that drag forces are a function of the Surface Area of each section, I'm not sure how to calculate the R term.. just by the coefficients?
R = "ratio of the Coefficient of Drag for the nose cone divided by Cd for the booster" = 0.06/0.31 = 0.1935
from your equation, assuming "a" is acceleration in G, a = (195-32.2)/32.2 = 5.05 G
Fsep (R=0.1935) = 5.05 * (18.5/(1+0.1935) - 12) = 17.5 lb (seems too low)
For comparison with R=0:
Fsep (R=0.00) = 5.05 * (18.5/(1+0.00) - 12) = 32.8 lb (seems to be a reasonable conservative value)
I'll take a stab at just summing the Cd values as a rough look...
or the nosecone/payload/altimeter bay "payload section" that would be:
Pressure Cd = 0.03, Base Cd = 0.00, Friction Cd = 0.07, Total Cd = 0.10
For the booster/fwd fins/aft fins "booster section" that would be:
Pressure Cd = 0.20, Base Cd = 0.22, Friction Cd = 0.14, Total Cd = 0.56
R = "ratio of the Coefficient of Drag for the "payload section" divided by Cd for the "booster section" = 0.10/0.56 = 0.1786
Fsep (R=0.1786) = 5.05 * (18.5/(1+0.1786) - 12) = 18.67 lb (seems too low)
I'm interested to hear what you think of the above. Hopefully I understood what you were saying and used the equation properly. I don't feel quite right about the R term still.
I set my finish to polished for everything. I've found that this gives the best match to my results with my Madcow 4" Fiberglass Level-2 rocket. My Open Rocket model should be from scratch.. I've measured and input all dimensions and weights etc. I may have started with my Level-2 rocket model and modified things from there. I can upload my model when I get home if you'd like to see it.