Has anyone done a comparison with altimeter apogee to open rocket time to apogee? I'm curious because I was reading on the PML site and they mention most simulations err on the side of negative 10-15% accuracy time to apogee. If that is the case one can probably get a better feel for delay times by subtracting an average of 12.5%.
This question actually decomposes into two questions:
1. What factors influence simulation quality?
The deciding value for the trajectory simulation is the expression Cd*rho*A, where Cd is the drag coefficient, rho is the density of the air and A is the cross section of the rocket. If you get that expression right, your simulation will be exact, even if each individual factor is completely wrong. As a result, winds aloft are irrelevant (at least to this order). If you underestimate drag, your sim will be wrong.
rho: Density changes are not that large. A density change of 10% corresponds to a temperature change of about 30K, or to an altitude change of about 1000m. So density alone cannot account for such large differences.
A: Relatively easy to measure, not much room for error.
That leaves as the main problem the Cd. Cd is difficult to measure (who has a wind tunnel in the basement?) and difficult to compute (sim programs disagree wildly about Cd). In addition, Cd ist not a constant. Cd during motor burn is much smaller than during coast due to the reduced base drag. So if you want accurate simulations, you should probably fly a few times and determine the matching Cd.
2. How large is the effect of an error in rocket data or atmospheric conditions on various parameters?
A simple way to determine these influences are the performance nomograms you can download from the resource section of the aerotech website:
https://www.aerotech-rocketry.com/c...ogs_Flyers_Data_Sheets/aerotech_nomograms.pdf. The nomograms show time to apogee and altitude depending on various parameters. I recommend that you have a look at the J350W diagram (attached), a motor familiar to many.
You'll notice that for a heavy rocket, a change in Cd, diameter or density has very little influence on the altitude or time to apogee. Changing Cd means you move vertically in the grid, and for large rocket mass, the curves are very steep, so a vertical change doesn't move you far away from one of the curves. The weight however has a very large impact. Make a 200g error on your 7kg rocket (thrust to weight is bad in this case, it's only an example), and your sim will be off 10%.
For light rockets, the diameter*rho*Cd becomes more important. With large diameter and/or drag, there even is a region where the time hardly changes with weight if the rocket is light enough. The same will happen with altitude if your rocket is even lighter, but most often, rockets are heavier. The upshot is that for light rockets you'll notice errors in the altitude before you'll notice errors in apogee time.
Since the altitude curves are always steeper than the apogee time curves, apogee time is always more affected by Cd/diameter/density errors, and altitude is always more seriously affected by mass.
In any event, a simple rule like "just subtract 10% from the delay time" is probably too simple. I'd rather try to find out where on the diagram your rocket is. The nomograms are grouped into nomograms for motors that one may want to use with a certain size of rocket. All nomograms in a group use the same scales, so your rocket (Cd/diameter/mass combination) is the some point on all nomograms. So simply put a transparency on top of the nomogram, and draw a point where your flight ended (time and altitude). After a few flights you should get a cloud of points that fairly well characterizes the average Cd of your rocket. You can then take that as the Cd for future simulations.
And we haven't discussed motor variance yet.
Best regards
Andreas Müller
View attachment j350w.pdf