## Rocket Motor Static Testing

### Introduction

It is one thing to develop a rocket motor that produces useful thrust, but it is another thing to know just how much thrust is generated. What is the shape of the actual thrust-time curve? Is the thrust constant throughout the burn, or does it vary greatly? What about chamber pressure? Is the maximum chamber pressure close to the structural limit of the motor? What is the total impulse produced? How does the actual (measured) performace compare to the theoretical (design)? In my attempts to answer these questions regarding the rocket motors that I developed over the years, a number of devices were devised. In this web page, I am presenting an chronological overview of these.

Measuring the actual thrust and chamber pressure over the duration of the burn can yield valuable information, not only about the motors's performance, but also the propellant's performance. Presented are the means to derive Total Impulse, Specific Impulse, C-star and Thrust Coefficient from the test data. These are some of the key parameters relating to the performance of a solid rocket motor and propellant.

### Thrustometer

One of the first successful rocket motors that I developed was the one that I used for my first amateur rocket flight. This was way back in 1972. This motor was relatively small, about 1.8 cm diameter by about 22 cm length. It was based on a similar, but shorter motor, that appeared to develop useful thrust, judging by the short burn time (about a second) and by the frightfully loud sound (at least compared to the model rocket motors that I had been familiar with!). But now that the motor seemed to be powerful, how could I find out just how powerful -- what thrust did it actually develop? Since thrust is a force, as weight is, why not use a scale? So my first static test stand consisted of a 25 lb (11 kg.) capacity scale against which the motor would push. I dubbed this contraption a "thrustometer" (Figure 1). I had simply secured a piece of pencil lead to the dial, which would etch against a sheet of paper that was taped to the face of the scale. As the dial would rotate under loading, it would etch an arc. In this way, the maximum thrust was recorded. This "thrustometer" worked surprisingly well, and was used for well over a dozen static tests. It finally met it's fate one day when a test motor built up excessive pressure, severed the safety pin, and blew out the end plug. The resulting "thrust" was well beyond the scale's capacity, and broke the dial off!

Figure 1 --Thrustometer used for earlier static testing

### Thrustograph

In a sense, the demise of the thrustometer was timely. Recording the maximum thrust was a big step in the right direction, and the burn time could be estimated from a tape recording of the firing. However, there was no way of telling what the shape of the time-thrust curve (thrust function) was. This was just as important to know, since the total impulse of the motor is basically the area under the time-thrust curve. Just how high a rocket will fly depends on the total impulse, and on the particular shape of the time-thrust curve rather than on the maximum thrust. As well, it is necessary to know the total impulse produced in order to determine the actual specific impulse of the propellant.
One type of instrument that is used to record a time varying function (such as that produced by a rocket motor) is a chart recorder. I decided to build my own version of such a device, which would measure the thrust directly, and for the full duration of the burn. I coined this apparatus that I built (with the help of my brother) a "thrustograph", which is shown in Figure 2.

Figure 2 -- Thrustograph in action -- static firing of the B-II motor, Dec.28, 1972
Click for details

The rocket motor was mounted horizontally on a sled which was allowed to move forward a short distance (under motor thrust) along a set of rails. The sled was restrained by a pair of powerful extension springs. Attached to the sled was an arm, which was attached at the other end to a pen holder. The pen was held such that the tip was in contact with a sheet of recording paper atop the thrustograph table. This recording paper (which was stored in rolled form) advanced along the thrustograph table by means of a feed mechanism, which consisted of a pair of steel rollers fitted with rubber rings, between which the paper was fed. These rollers were driven by a 120V electric (furnace) motor turning at 1720 RPM. The rotational speed of the rollers was reduced, however, through a series of belts and pulleys such that the paper feed rate was 4.50 inches per second (11.4 cm/s.).

Just prior to firing the motor, the paper feed was activated. As the motor fired, the thrust would overcome the spring force and move forward. The actual distance the sled would move was determined by the spring constant (stiffness). Typically, the springs were selected such that the maximum movement was no greater than about 6 inches (15 cm). The paper width was 8.5 inches (21.6 cm). The movement of the sled combined with the feeding of the paper over the table caused the pen to trace a curve which corresponded to the thrust-time curve of the motor. An example of such a plot is shown in Figure 3.

Figure 3 -- Example of a plot obtained from the Thrustograph (force along vertical axis, time along horizontal axis).

Calibration of the springs was done by either of two methods. A pair of angler's scales of 50 lb. capacity (each) was used to extend the thrustograph springs by a certain distance (d) and by observing the total force (F) required, the spring constant (k) was determined (k=F/d). The second method was simply to remove the springs from the thrustograph and hang weights from the end, and measuring the displacement to obtain the spring constant. These methods were fine for motors of, say, less than 200 lbs (900 N.) thrust, but were impractical to do with springs of greater stiffness.
Overall, the thrustograph worked well, and was used for many static tests. It's main limitation, however, was that it was pretty much limited to motors of relatively low thrust ( < 200 lbs.). Fitting the device with stronger springs that would be necessary for motors of several hundred pound thrust seemed to be beyond the practical limits of the thrustograph. Clearly, it appeared necessary to devise a more universal static testing rig that would be suitable for motors of just about any size and power.

### Static Test Rig

Construction of the Static Test Rig (as I came to refer to it ) was begun in early 1982. This device was built as a replacement for the thrustograph, and, of robust construction, was intended as a tool that would have the capability of handling rocket motors of much greater thrust than its predecessor could ever handle. The principle of how this device worked was significantly different -- rather than directly plotting the thrust-time curve, as the thrustograph did, this device would convert thrust to an electronic signal that would be collected and processed by computer . At the heart of the system was a force transducer, salvaged from a digital bathroom scale. This was essentially a small cantilever beam fitted with four strain gauges. As the beam was deflected, the strain gauges would undergo a change in electrical resistance. A conditioning circuit would convert this to a change in voltage, an Analogue-Digital (A/D) converter circuit would convert this to a binary signal, which was read by computer and stored on digital tape, for postprocessing. The signal sampling rate was a generous 580 samples/sec.

 The rocket motor was mounted vertically, with the nozzle facing upward, in a tubular holder. The bottom of the holder sat on a deflection bar which acted as a beam supported at both ends, with the load (motor thrust) acting downward at the middle of the beam (detail). The force transducer was mounted such that it's end was in contact with the deflection bar near the middle. As the motor would fire, the thrust would force the deflection bar to deflect downward, and in doing so, also deflect the beam of the force transducer.
The deflection was generally limited to about 0.25 inch (6.4mm), and so the bar was selected such that its stiffness under maximum thrust did not exceed this limit. A "stop" was fitted under the deflection bar to physically limit the deflection, in order to prevent damage to the bar and force transducer in the event of over-thrusting or a blow-out. The supporting structure of the rig was of heavy I-beam construction fitted with three tubular legs welded to the I-beam ends.

During trial testing of the rig with simulated loads applied, it was found that oscillation was a significant problem. Instead of the smooth curve that was expected, the curve was full of high frequency oscillations, as a result of being highly underdamped, much like a spring that would oscillate up and down if a heavy weight was suspended from it. After much consideration (including the possibility of eliminating the oscillation through software means) it was decided to design and build a hydraulic damping device which would be attached to the deflection bar. The damper was made such that the amount of damping could be easily adjusted, as required.

The deflection bar chosen on the basis of deflection at it's midspan, due to the motor's maximum thrust. The deflection is given by:

where y=deflection at midspan, F=motor thrust force, L=bar length, E=modulus of elasticity of bar, b=bar width, d=bar thickness.

Calibration of the static test rig was performed with the aid of a calibration arm with various weights hung at its end. The arm effectively amplifies the force due to the weights, with this force applied at the deflection bar midspan (where the motor thrust acts), as shown in Figure 6.

Figure 6 -- Calibration arm setup. F=force applied to deflection bar, W=weight attached to end of calibration arm, Wa=weight of calibration arm

Example of Thrust-time curve from data obtained using the Static Test Rig.

### STS-5000 Static Test Stand

The Static Test Rig worked reasonably well but did have a couple of drawbacks. The need for a damper to prevent oscillations was one drawback, but more importantly, it was an inconvenience to have to change the beam to suit different motors of different thrust levels. Perhaps its biggest drawback was its lack of portability. It was heavy and unwieldy to transport. In 2000 I was in need of a test stand for firing my newly designed Kappa (K-class) solid rocket motor. So I set out to design one. Portability was an important consideration. As was the desire to have it accommodate a load cell for thrust measurement. Such a load cell could be hydraulic or electronic. The outcome of this effort was the STS-5000 Static Test Stand. This test stand was designed for testing motors with a maximum thrust of up to 5000 Newtons (1100 lbs.). The basic construction of the STS-5000 Static Test Stand is a tripod-based stand fabricated of metal tubes fastened with bolts. It was very lightweight, strong and stiff, low-cost and could be readily dismantled for transport and setup in the field. Now 20 years later, I still use the STS-5000 Static Test Stand for performance test of nearly all my new motors.

Click for complete details:    STS-5000 Static Test Stand web page

Left: STS-5000 Test Stand for static test KDX-002 (July 2000)
Right: STS-5000 Test Stand for static testing of experimental Impulser-B motor (May 2020)

### Total Impulse and Specific Impulse

The measurement of thrust of a rocket motor yields important information that can be used to determine how high and how fast a rocket will fly. But much more than that, the thrust data can be used to calculate Total Impulse and Specific Impulse. Knowing the actual "delivered" values of these two key parameters of rocket motor performance allows a comparison with the design values. In particular, these two parameters informs the experimenter as to how well the motor and propellant combination performed. For example, if the delivered Specific Impulse is significantly lower than expected, the cause may be either a shortcoming relating to the motor design (such as an inefficient nozzle), or a deficiency in the propellant (such as how it was prepared). Measuring Total and Specific Impulse also allows the experimenter to assess the effect of making modifications to the motor or propellant. For investigating new propellant formulations, delivered Specific Impulse provides a direct indication of performance.

Click for complete details:    Determination of Total and Specific Impulse from Test Data

### Chamber Pressure, C-star and Thrust Coefficient

Measuring rocket motor chamber pressure during a static firing yields important information about the motor's performance that is of equal value to that of thrust measurement. The self-evident value of pressure measurement is the opportunity to compare between design and delivered chamber pressure. Why is the measured chamber pressure higher (or lower) than expected? Does the pressure ramp up and tail off as expected? Having hard data allows the experimenter to make a rational investigation into why there's a discrepency. Slow ramp-up is often a consequence of underpowered igniter. An extended tail-off period could mean that there was delayed ignition of some propellant surface regions. Lower overall chamber pressure is often related to some particular aspect of propellant preparation, such as oxidizer particle size.

There are two additional performance parameters that can be derived from the measurement of chamber pressure -- Characteristic Velocity, usually referred to as c-star, and thrust coefficient. C-star is a figure of thermochemical merit for a particular propellant and is indicative of combustion efficiency. C-star can be calculated from the measured chamber pressure values and compared to theoretical value, typically obtained from ProPEP or a similar propellant evaluation program. The thrust coefficient, which is a factor that relates chamber pressure and thrust, may be calculated using the measured values of these two parameters. The thrust coefficient reveals to the experimenter how well the nozzle "amplifies" the thrust that would be obtained if the nozzle were a simple hole.

Another benefit of measuring chamber pressure is that the data can be used to get a reasonably good estimate of the motor thrust, if thrust is not being measured directly. As chamber pressure and thrust are directly proportional, related by the thrust coefficient and throat area (both of which may be considered constant), a preliminary estimate of thrust over the full duration of the burn can be obtained.

If this equation, the thrust (F) corresponding the the measured pressure (Po) is obtained by multiplying pressure by the thrust coefficient (Cf) and throat cross-sectional area (At). For a well-designed and reasonably well-made steel nozzle[1] the thrust coefficient can be conservatively taken as Cf=1.5 for sugar propellant. Throat area is obtained from the measured diameter. Measuring solely chamber pressure is a good strategy for new motor designs, as it avoids potentially destroying an expensive load cell if the motor should overpressurize and blow out the nozzle or bulkhead.

Click for complete details:    Measuring Chamber Pressure and Determination of C-star and Thrust Coefficient

[1] 1000 psi operating pressure; 30o convergent half-angle;12o divergent half-angle; expansion ratio >8