Problem with maximum ceiling calculations

[HattoriHanzo]

I try to calculate maximium altitude for some famous rockets like Super Loki, Sidewinder Arcas, Sparrow Arcas etc. Some incorporates a second stage. I use formulas derived by"mk" and from Sutton, also use the simulation program: http://webalt.markworld.com/usermotor.html

I know that all these formulas are for ideal circumstances.
My answer seems to be all wrong. I only get around half the stated maximum ceiling for these rockets. I dont do anything wrong with the mathematics. I also have tried numerous of assumptions(like stage delaying, drag coefficient and stuff like that) from very small numbers to very high.

What am I doing wrong/dont understand here?

[mk]

I don't know at which elevations you're dealing. Maybe the change in gravitative acceleration konstant for the earth becomes important? but that should not necessarily give figures of 50% less the stated elevations.
Of course supposed those rockets won't leave the earth's field of gravitation (what is impractical today with single staged rockets).

Anyway, a certain elevation range example for one of the rockets you're studying, Hattori Hanzo, would be nice. Just to get an idea, due I'm by no means familiar with details of such rockets around.

And, are the calculations you do with the methods are all in same range, or do they differ quite badly?
I posted the derivation steps, thus correcting a mistake should be possible for everyone who would spot one.

[HattoriHanzo]

Hi mk,

Heres some important information on the Super Loki

Launch Weight: 68 lb
Burnout Weight: 31 lb
Instrument Dart Weight: 18 lb
Booster Weight: 50 lb
(A 4.5 lb ballast weight is added to the booster for launches near populated areas. The ballast gives the booster aerodynamic stability on descent)
Propellant: ammonium perchlorate based
Burn time: 2.1 seconds
Aero Dyne SR110-AD-1 with thurst 25kN.
Height, Total: 10.5 ft
Height, Booster: 6.5 ft
Height, Instrument Dart: 4 ft
Booster diameter: 4 inches (excluding fins)
Altitude for booster/dart separation: approx 30,000 ft
Maximum Altitude (instrument dart): approx 250,000 ft
(185,000 ft w/ballast)
Time to apogee: 110 to 120 seconds
Top speed: 1 mile/sec (approx. mach 5)
Spin rate during ascent: approx 16 rev/sec (1000 rpm)
Payload: (main portion) 1 11/16 inch dia. x 11.2" long
Payload descent time: to 20km: 30 - 45 min with 10ft starute
to ground: 1.5 + hours (weather dependent)
Max Payload Weight: 4 lb (but is typically about 1 lb)
Initial acceleration (vertical): 60 g's (up)
Initial coasting acceleration due to air resistance: approx 30 g's (down)
Maximum centripetal acceleration on payload: 20 g's (horizontal)
Acceleration upon ejection: 100 to 250 g's along trajectory

[Jim Berquist]

When in dought try it out!!

Use a altimeter.....FM..and or am ..

a simple FM transmitter with a vco will tell you the truth..

You can build a altimeter little or less...check it out!!!

a hint: ne555...2n2222......002pf......three turns of 30swg wire....0 to 40 pcf
variable cap....conductive foam..foil...electodes........

this will send a fm freq relitive to alt and can be calculated to alt once you know the barometrics of said toy.....

jim