A Short Survey of Off-The-Shelf Solid Motors for Orbital Upper Stages

A Short Survey of Off-The-Shelf Solid Motors for Orbital Upper Stages

By Ed LeBouthillier

Many suggest using off-the-shelf solid motors (or similar custom motors) for upper stages of small orbital launchers. In this discussion, I review some of the requirements for upper stages and the possibility of using solids as upper stage motors. I will presume that a basic 1/4 pound (113 gram) payload is selected.

OFF THE SHELF MOTORS

High Power rocketry uses motors that provide many benefits for someone considering upper stages for orbital launchers. They are efficient, use modern propellants, come in a wide range of impulses and require little development.

The following table lists a few different solid motors that might be suitable for upper stages and their parameters:

Manuf.	Model	Total Impulse (N-s)	Propellant Weight (grams)	Loaded Weight (grams)	Empty Weight (grams)	BP Ratio (λ)	SL Isp	Vac Isp
Aerotech	I305	450	302.1	581	278.9	0.92	150 s	211 s
Cesaroni	I303	538	270.0	500	230.0	0.85	189 s	235 s
Aerotech	I350R	2500	1400.0	2294	894.0	0.64	189 s	235 s

( Note: BP Ratio = Empty Weight/Propellant Weight )

Let me explain how I estimated the specific impulses for sea level (SL) and vacuum (Vac) exhaust pressures.

First, the sea level Isp is derived from the published data (and verified as being reasonable). The equation is:

                                    Avg Thrust * Burn Duration

            Ideal Isp =        --------------------------

                                         Propellant Mass

These propellants are specified as being composite propellants. I used Propep as the

combustion code to estimate the Isp. I put Ammonium Perchlorate and HTPB into ProPep. I then set the mixture ratio similar to what is published as commonly used. I presumed that the published value represents 90% of the theoretical maximum Isp. Therefore, if 150 seconds is the value derived from published figures, then the theoretical ideal value of the Isp is 150 seconds / 0.90 = 166 seconds. I then adjusted the chamber pressure in Propep until I got a theoretical value equal to this Ideal Isp. I then calculated the Isp in a vacuum using Propep and then multiplied that value by 90% to get the vacuum Isp. It’s rough, but it gives meaningful statistics for comparison.

IMPLICATIONS

Based on the above figures, we can estimate the likely delta V from one of these motors.

If we presume no payload, and just the motor weight, then using the Aerotech I350R as an example we have:

            dv = g * Isp * ln( Mf / Me )

            dv = 9.8 * 235 * ln( 2294 g / 894 g )

            dv = 2303 * ln( 2.57 )

            dv = 2303 * 0.94

            dv = 2164.82 m/s (7102 fps)

Since we need to provide about 7467.6 m/s (24500 fps) to 7772.4 m/s (25500 fps) in the upper stages, we would need about 7772 / 2165 = 4 stages at this performance level (for a total of 5 stages with a first stage). Presuming a 113 gram payload, a 113 gram guidance and control system for the 5th stage, we have:

	Stage 5	Stage 4	Stage 3	Stage 2	Stage 1
Oxidizer	AP	AP	AP	AP	Lox
Fuel	HTPB	HTPB	HTPB	HTPB	Propane
Payload	0.113	2.5	39.5	619.5	9704.6	kg
OF Ratio	2.333	2.333	2.333	2.333	2.200
Oxidizer Density	1.949	1.949	1.949	1.949	1.141	g/cc
Fuel Density	0.919	0.919	0.919	0.919	0.582	g/cc
Avg Density	1.640	1.640	1.640	1.640	0.966	g/cc
Average Isp	235	235	235	235	252	seconds
Desired DeltaV	1867.4	1968.3	1968.3	1968.3	3172.7	m/s
Body:Fuel Mass (λ)	0.72	0.63	0.63	0.63	0.197
Payload Ratio	0.047	0.068	0.068	0.068	0.155
Structural Coef	0.419	0.387	0.387	0.387	0.165
Propellant Ratio	0.581	0.613	0.613	0.613	0.835
Mf/Me Ratio	2.249	2.349	2.349	2.349	3.610
Propellant Mass	1.402	22.711	356	5574	52152	kg
Oxidizer Mass	0.981	15.897	249	3901	35854	kg
Fuel Mass	0.421	6.814	107	1672	16297	kg
Oxidizer Volume	503.2	8154.5	127748.1	2001297.1	31423640.1	cc
Fuel Volume	457.3	7410.7	116096.3	1818760.5	28004727.9	cc
Stage Weight	2.411	37.018	580	9085	62425	kg
MT	1.009	14.308	224	3511	10274	kg
Me	1.123	16.832	264	4131	19978	kg
Mf	2.524	39.542	619	9705	72130	kg
Stage Impulse	3230	52338	819926	12844938	128880945	N-s
Cum delta V	1867	3836	5804	7772	10945	m/s

The important thing to notice is that the size of the 3rd stage is quickly too large (close to 620 kg [1370 lbs]). By the time you get to the second stage, it is up to 9705 kg (21000 lbs). The reason is that the performance is too low and weight too high for these motors. For a tiny 113 gram payload, the exo-atmospheric stages are 9705 kg.

SUMMARY

Based on this quick survey of a few commercial rocket motors (yes, it’s a small sample but I think it’s representative), we can see that typical off-the-shelf motors are likely too low in performance and too heavy for orbital launchers. This is not to say that these motors are not of high reliability and capability: they are highly engineered and quality products developed for the commercial market. They are safe and reliable and often reusable. However, these design choices work against them being the lightest possible and what is needed for orbital vehicles.