Propulsion:

The Mark X has a 98mm motor mount capable of supporting motor casings up to 53 inches in length allowing the rocket to fly on a variety motors.  A 75/5120 NS motor casing loaded with a 75mm Aerotech M1297 W reload with a total thrust of 5,417 Newton-Seconds (NS) will be used on the certification flight.   The motor has an average thrust is 1,304 NS and a burn time of 4.17 seconds.  Positive motor retention for this flight is accomplished through use of an AreoPack 98mm motor retainer and a 98-75mm adapter.

Simulation results:

The simulation results in the table below display some performance characteristics of the Mark X.  They were generated using RockSim 8.0 and the cd was set to be calculated at the time of the simulation .  This is presented merely to show the versatility of the Mark X rocket.

Sim #	Motor	Max alt.	Max velocity	Max accel.	Apogee
1	AMW K975 ww	1,745'	315 ft / sec	1070 ft / sec2	11.30
2	AT    K1050 w	1,920'	334 ft / sec	1072 ft / sec2	11.66
3	AT    M1297 w	5,922'	642 ft / sec	1079 ft / sec2	19.48
4	AMW M1350 ww	5,930'	650 ft / sec	1073  ft / sec2	19.64
5	AT    M1315 w	7,385'	715 ft / sec	1076  ft / sec2	21.72
6	AT    M1419 w	8,300'	740 ft / sec	1073  ft / sec2	23.64
7	AT    M1939 w	11,655'	980 ft / sec	1073  ft / sec2	26.51
8	AT    N2000 w	13,780'	1110 ft / sec	1074  ft / sec2	28.11

Simulation 3 Details:

This simulation's configuration is identical to one the Mark X will use in the level 3 high power certification attempt.

Motor selection:
Impulse class	M
Manufacturer	Aerotech
Average thrust	1,304 Netwons
Total thrust	5,434 Newton-Sec.
Diameter	75mm
Propellant	White lightning
Average burn time:	4.17 Sec.
Launch conditions:
Altitude:	500.00 Ft.
Relative humidity:	75.00 %
Temperature:	85 Deg. F
Pressure:	29.91 In.
Wind Speed Model:	Light (3-7 MPH)
Low wind speed:	3.00 MPH
High wind speed:	7.90 MPH
Wind turbulance:	Some variability (0.04)
Frequency:	0.04 rad/Sec.
Wind starts at altitude:	500.00 Ft.
Launch guide angle:	0.00 Deg from vertical
Latitude:	1.571 Deg
Launch guide data:
Launch guide length:	144.00 In.
Velocity at launch guide departure:	75.23 Ft./Sec.
The launch guide was cleared at:	0.33 Sec.
Minimum velocity for stable flight:	44.00 Ft./Sec.
Stable flight reached at:	59.09 In.
Max Data values:
Maximum acceleration:	Vertical (y): 1078.85 Ft./Sec.2 Horizontal (x): 1.73 Ft./Sec.2 Magnitude: 1078.85 Ft./Sec.2
Maximum velocity:	Vertical (y): 641.616 Ft./Sec. Horizontal (x): 11.59 Ft./Sec. Magnitude: 642.49 Ft./Sec.
Maximum range from launch site:	530.67 Ft.
Maximum altitude:	5922.61 Ft.
Recovery system data:
Drogue parachute deployed at:	19.48 Sec.
Velocity at deployment:	23.58 Ft./Sec.
Altitude at deployment:	5922.61 Ft.
Range at deployment:	-456.25 Ft.
Main parachute deployed at:	73.18 Sec.
Velocity at deployment:	91.934 ft/s
Altitude at deployment:	999.95 Ft
Range at deployment:	-152.70 Ft.
Time data:
Time to burnout:	4.17 Sec.
Time to apogee:	19.48 Sec.
Optimal ejection delay:	15.310 Sec.
Landing data
Time to landing:	137.32 Sec.
Range at landing:	530.67 Ft.
Velocity at landing:	Vertical: -15.3431 Ft./Sec. Horizontal: 9.4666 Ft./Sec. Magnitude: 18.0285 Ft./Sec.

Separation and deployment charge sizing:

Step 1: determine the force necessary to separate the airframe and deploy recovery devices.
		1 #2-56 nylon screw requires ≈ 35 lbs. of force to break 4 #2-56 nylon sheer pins will be used for each stage of recovery to prevent drag separation during flight
	Equation:
		F = (x * 35) + s F = Force (in lb.) x  = # of sheer pins s = safety margin (in lb.)
	Solution:
		x = 4 F = (4 * 35) + 60  F = 200 lb.
Step 2: Determine pounds per square inch (PSI) necessary to exert 200 lb. force.
	Equation:
		PSI = F / (pi * d) F = Force (in lb.) As = Surface area of bulkhead = pi * d d = Bulkhead diameter (in In.)
	Solution:
		F = 200 lb. pi = 3.14 d = 7.61 In. PSI = F / (pi * d) PSI = 200 lb. / (3.14 * 7.61 In.)   PSI = 8.37 In.2
Step 3: Determine correct charge size to generate desired PSI
	Equation:
		Wbp = C * D2 * L Wbp = Weight of black powder needed to attain desired PSI (in g) C = PSI * 0.0004 D = Airframe diameter (in In.) L = Compartment length (in In.)
	Solution for Main Recovery Charge:
		C = 0.003348 D = 7.61 In. L = 24 In. Wbp = C * D2 * L Wbp = 0.003348 * 7.612 * 24   Wbp = 4.65 g
	Solution for Drogue Recovery Charge:
		C = 0.003348 D = 7.61 In. L = 12 In. Wbp = C * D2 * L Wbp = 0.003348 * 7.612 * 12   Wbp = 2.33 g

Main parachute sizing:

	Equation used to attain a 15 Ft./Sec. descent rate:
		dm = [39.6 * √(w * 0.454)] / 12 dm = main parachute diameter (in Ft.) w = rocket weight after motor burnout (in lb.)
	Solution:
		w = 44 lb. dm = [39.6 * √(w * 0.454)] / 12 dm = [39.6 * √(44 * 0.454)] / 12 dm = [39.6 * √(19.967)] / 12 dm = 176.9903 / 12  dm = 14.7492 Ft.

Drogue Parachute sizing:

	Equation used to attain a 50 Ft./Sec. descent rate:
		dd = 24 * √(w * 0.140) dd = drogue parachute diameter (in In.) w = rocket weight after motor burnout (in lb.)
	Solution:
		w = 44 lb. dd = 24 * √(44 * 0.140) dd = 24 * √(6.160) dd = 24 * 2.482  dd = 59.566 In.

Avionics Bay vent hole sizing:

	Equation:
		dn = dt * √[( Aref / Vref ) * ( l / n )] n = number of static port holes dn = diameter of individual static port holes for n # of holes (in In.) dt = diameter of compartment (in In.) l = length of avionics compartment (in In.) Aref = reference to area of static port in the static port sizing rule of thumb (in In.2) Vref = reference to volume of compartment in the  static port sizing rule of thumb (in In.3)
	Solution:
		n = 8 dn = diameter of individual static port holes for n # of holes (in In.) dt = 7.51 In. l = 17 In. Aref = pi * (0.25 / 2)2 = 3.14 * (0.125)2 = 0.049 In.2 Vref = 100 In.3 dn = 7.5 * √[( 0.04906 / 100 ) * ( 17 / 8 )] dn = 7.5 * √[( 0.0004906 ) * ( 2.125 )] dn = 7.5 * √[0.001043] dn = 7.5 * 0.03229   dn = 0.242 In.