New: 1/8/99
The following article is a sample student paper taken from the book "Composition for Technical Students", by J. D. Thomas, with copyrights of 1942 and 1957. Included in the text is a graph of RPM vs Horsepower, dated 1942, meaning that the Brown model engine wasn't very old at the time.
The article is interesting reading, and the theory plus implementation of the dynamometer are well within most modeler's capabilities. You should be able to determine torque and horsepower for rubber motors, electrics or gas/glow/diesel engines using this process.


By E. H. Badger, Jr


It was desired to devise and construct a dynamometer suitable for determination of the speed and power characteristics of small internal combustion engines and to run actual tests on a Brown model airplane engine. This engine has a 7/8 inch bore and 1 inch stroke, with a displacement of 0.60 cubic inch. It is rated at 1/5 horsepower. A 12.8 inch and a 14 inch propeller were to be used as load for two series of runs, and a curve was to be plotted of speed versus horsepower for each propeller, over the normal operating range of the engine.

The dynamometer selected had to be simple to construct and to use, while being capable of measuring as accurately as possible the output torque of the engine under actual operating conditions. The brake or other absorption type dynamometers commonly used for internal combustion engine tests could not be applied because of the size and operating characteristics of the midget engine. Therefore, a reaction type dynamometer was selected. It was naturally adaptable to the requirements of the test, allowing operation of the engine under the load of its own propeller and providing for sensitive torque determination.

Since any loss of power to the speed determining instrument might cause an appreciable error on account of the small total output of the engine, a Strobotac was selected for determination of the speed of the engine during the tests. The use of his instrument allowed accurate speed determination by reflected light and introduced no load error to the calculations for horsepower output of the engine.[In the 1990s, we can use a readily available, inexpensive tachometer. / AL]

The problem of materials for the construction of the dynamometer, tools and equipment for construction, and instruments for tests was easily solved, since the facilities of the university's engineering shops were at the disposal of the test crew.


The output-horsepower formula for engines is:

Horsepower = (2pi x T x N) / 33,000 = K x T x N

The K is a constant for all test calculations. The T represents load torque in pound-feet units. The N represents the speed of the shaft rotation in revolutions per minute. Torque and speed must be measured under varying operating conditions as a basis for calculation of data for engine performance curves.

In this test, a reaction dynamometer was designed and built to measure the torque. The reaction principle was better, in this case, than the usual system of absorbing the output of the engine in a friction Prony brake or other output absorption device for torque measurement. Prony brakes are not adaptable to high speeds, and all the absorption setups would have required the use of a flywheel rather than the air propeller normally used on the engine. The flywheel load was undesirable, because the engine would not have been operating under normal conditions, and also because of difficulty in properly cooling the cylinder. The reaction type dynamometer measured the reaction torque, which, by Newton's third law, is exactly equal and opposite to the output torque of the engine. The manner of torque determination by the dynamometer designed for this test may be explained by reference to Figure 1.

The engine was fixed on a cast iron mounting block and the whole unit was pivoted about pin bearings in the block as shown. A light torque balance arrangement with a 20 inch balance arm and a 0.224 pound movable trimmer weight was bolted to the block so as to rotate with the engine. The system was balanced under static conditions without the adjustable trimmer weight. Then, when the engine was running at the desired speed, the torque balance trimmer could be run out on the arm until the pointer stayed on the zero mark. Under these conditions the torque being delivered to the propeller was equal to the weight of the trimmer balance multiplied by the distance A, or WA pound-feet. Actually, distance L was noted in data taken during the tests, because that length could be easily measured with a steel rule during the tests; the use of this system eliminated the necessity for calibrating the balance arm directly. Then the required distance A was computed from the equality:

A = (D - B/2) -L

The bearings about which the block rotated were merely 0.4 inch pin bearings made as frictionless as possible and well oiled. The natural vibration of the engine and block was depended on further to reduce errors due to static friction. The motor ignition wires had to be loose and were brought in close to the rear pivot so as not to introduce torque errors.

There is an error with this type of dynamometer due to the whirling slipstream caused by the propeller, which reacts against the engine and supporting structure, resulting in inaccurate torque readings. The factors involved in a correction of this error are: diameter, pitch, number of blades, and speed of the test propeller; form of engine; design of test stand; and size and shape of the enclosure or nacelle in which the engine is run. Such a correction is obviously difficult to determine accurately. If the error is considered great enough to require correction, the slipstream is usually straightened out by inserting a honeycomb, or grid, between the engine and the propeller, rather than by calculating a correction factor to be applied to the horsepower formula. As affecting the test results included in this report, the error above mentioned was considered to be small and, because of limited time, was entirely neglected.

The Strobotac used for speed determination allowed measurement of speed without the imposition of any load on the engine and therefore introduced no error in results. lhe Strobotac is an electrical instrument which is, in principle, a neon light flashing at a controllable frequency. A knob adjusts the frequency over the range of the instrument, 600 to 14,500 vibrations per minute, and the frequency at any instant is read on a dial on the top of the instrument. When this instrument is pointed toward a piece of rotating or oscillating equipment and adjusted to the frequency of rotation or vibration of that piece, the apparatus seems to stand still. This phenomenon is due to the fact that the piece is lighted only when it is in one position of its cycle. An error of an exact multiple or fraction of the speed may be made with this instrument when it is used to measure the rotating speed of such a piece as the two-bladed propeller of this test, since there is a possibility of the propeller seeming to stand still if the Strobotac should be emitting light at a frequency to bring the propeller into view at every half revolution, or at every second or third revolution, etc. With some experience an operator is not likely to make such a mistake, but a Jagabi tachometer was used to check the speed range of the Strobotac in these tests. The Jagabi is a direct-reading tachometer which has a rubber cap to be pressed onto the end of the shaft of the engine. When a button is pushed down on the Jagabi, the needle moves around the dial to the speed cf the shaft and stops. In principle, the Jagabi is merely a timing device which allows a needle to travel at a certain fraction of the shaft speed for a predetermined constant time interval, so that when it stops it is indicating shaft rotation (in revolutions per minute) on the dial. The Jagabi, like all other mechanical speed measuring devices, robs the shaft of a certain, though small. amount of power.


Brown Model D-806 midget engine with ignition system and propellers; Strobotac No. 2898, speed range 600 - 14,500 rpm; Jagabi Tachometer No. 69027, speed range O - 10,000 rpm.

Materials for dynamometer:
One l 1/2" x 2 1/2" x 4" cast-iron block for motor mount
One 3/4" x 1 1/2" x 1 1/2" cast-iron block for trimmer balance
One 1/4" x 3/4" x 1" boiler-plate steel for balance weight
Two 3/16" diam. rods for balance arm and pointer unit
Two 1/8" diam. rods for balance arm and pointer unit
One 1/4" x 2" x 9" boiler plate steel for motor mount base
One 1/2" diam. x 1" mild steel for front pivot
One 1" diam x 3" mild steel for rear pivot bolt
One l/2" nut for pivot lock
Four 3/4" screws for mounting base on table
Six 1/16" brass bolts for motor mount and balance unit attachment

Tools & equipment for construction:

Cincinnati milling machine with circular milling saw cutter
Ram-type reciprocating shaper
Lathe with thread-cutting attachment
Oxyacetylene welding outfit with brazing rod and flux
Analytical balance scales and weights
Hammer, grinder, hacksaw, crescent wrench, screwdriver, pliers, etc.


The first step after designing the system was the construction of the dynamometer. The base, which was to form the cradle for the motor mount block, was cut from a piece of mild steel boiler plate with a hacksaw. It was heated with an acetylene torch and bent to shape in a vise with a hammer. The rear vertical part of the base was bent double and brazed together to provide for a longer threaded hole for the mounting of the adjustable pivot bolt. The mounting holes and bearing pivot holes were drilled and the rear pivot hole was tapped for the adjusting bolt. The cast-iron motor mount block was then made. After being squared up, it was clamped in the milling machine and grooved to hold the crankcase of the engine. The engine mounting holes and balance-arm bolt holes were drilled and tapped. The piece was then chucked up in a lathe, and the female pivot impressions were bored in place in each end. The mild steel for the front pivot was clamped in the lathe chuck and the pivot turned to size. This piece was then brazed in place in its hole in the base piece. The steel for the rear pivot bolt was chucked up and turned to shape. The handle was knurled and the threads were turned as shown in Figure 2.
The welding rods from which the balance-arm unit was made were bent to shape and brazed together. The attaching tabs were heated, flattened to shape with a hammer, and drilled for the attaching bolts. Then the entire setup was assembled and screwed to a table, and a vertical line was marked directly under the center line of the engine as a zero mark for the pointer. A small weight was brazed on the free arm of the balance system and additional brazing rod melted on it until the system was perfectly balanced. The adjustable trimming balance weight was formed on the shaper and slotted with the saw in the milling machine. It was drilled and tapped for the clamping wing bolt and accurately weighed with the bolt in place.

Figure 3 shows the final assembly, after the ignition system had been attached to the engine. The pivot bearings were oiled, and the Strobotac was adjusted and set up in front of the propeller, completing preparations for the test.

The engine was started and two interlaced series of runs were made, one with each of the two propellers. (See Appendix at end of text below.) The distance L and the shaft speed were taken for each run of each series. During the tests Operator I read the Strobotac and the Jagabi, Operator II adjusted the engine and operated the balance arm, and Operator III recorded the data. After nineteen runs had been made, the Strobotac was removed and twelve more runs were made with the Jagabi revolution counter being used for speed determination. Actually, it was found that these readings checked very closely with those taken by the Strobotac, though the Jagabi had been intended only to give the approximate speed range of the Strobotac.


The results of the tests are illustrated by the graph.

The larger propeller absorbs a given horsepower at a lower speed than the smaller one. The speed curves show that the horsepower absorbed by the propeller is approximately proportional to the square of the speed for either propeller. The maximum horsepower output noted for the engine on these tests was 0.298 horsepower at a speed of 5710 rpm; this result was obtained with the 12.8 inch propeller. The largest horsepower obtained with the 14 inch propeller was 0.257 horsepower at 4750 rpm. The engine, which is rather sensitive in operation, was not working as well as it should have been during the test runs. Some ignition trouble was present, and it is believed that a greater output and speed could have been obtained by further adjustment and tests. However, the curves illustrate the normal operating range of the engine. (See graph and tables.)


Though the Strobotac, when properly adjusted and skilfully used, unquestionably gives the better speed determination, the speeds taken with the Jagabi checked very closely in this case. In fact, the points determined by the Jagabi speed runs were accurate enough to be used as some of the points determining the curves of this report. The Jagabi is the easier to use of the two instruments and probably absorbs only a very small amount of power.

Improvement in the accuracy of results might be made by installing ball or tapered roller bearings to reduce the friction in the pivots of the engine block. Another refinement could be made by the use of a grill-work to straighten the slipstream passing the motor.

This type of dynamometer is commonly used for factory performance tests of nearly all aircraft engines, but is not ordinarily used for other types of engines. An interesting special use of the principle is an application to aircraft engines in actual airplane installations. When so applied, the system affords an accurate indication of the actual performance of the engine at various attitudes and altitudes of flight. Such results could not be obtained by test-block methods because of the variable temperatures, air densities, and humidities and other similar conditions that an aircraft engine encounters in service. The torque indicator is incorporated as an integral part of a planetary reduction gear system between the crankshaft and the propeller, and is similar in principle to the reaction dynamometer described in this report. The annular gear surrounding the planetary gear system is anchored to two pistons which operate in oil-filled cylinders. The reaction of the annular gear is transmitted to the oil in these cylinders, and the resulting pressure is indicated on a gage calibrated in pound-feet torque. This gage reading, together with the reading of the gage of the direct-driven tachometer of the engine, gives data for determination of the horsepower being delivered by the engine to the propeller under any condition of operation in flight. It is possible to design an instrument which will utilize the oil pressure from the torque cylinders and the tachometer speed to give a direct horsepower reading on the dial of a gage during flight.

Runs With 14" Prop
Run No.N=rpmL=inchesA=feetHP

Runs With 12.8" Prop
Run No.N=rpmL=inchesA=feetHP