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There is a fine line between recklessness and courage.


During a run, vehicle speed increases until the engine power at the driving wheels is no longer greater than the power required to overcome the sum of aerodynamic drag and rolling resistance. Maximum possible speed occurs when the overall drive ratio is chosen so that the engine is at peak power rpm when the resistance power is equal to the available engine power. This operating point, however, will probably not be reached before the end of the track is reached. Thus the overall gear ratio must be chosen to yield the highest possible average speed in the fifth mile. This is ultimately done by trial and error, but computerized modeling can provide valuable guidance that will hopefully reduce the number of trials and errors. Land speed racing is a lot like drag racing. To realize maximum speed, you cannot afford to waste any time or distance when you could be accelerating.

Sample results of a physics-based computer program that returns elapsed time, speed, engne rpm, acceleration, and indication of wheel slip, as a function of distance for specified input parameter values.

My streamliner is a solo motorcycle designed to compete in land speed record attempts in the S-G-650 class, at events such as those held at the Bonneville Salt Flats sanctioned by SCTA/BNI, AMA/BUB, and FIM. To estimate top speed, I developed a computerized analysis to calculate speed, distance, elapsed time, acceleration, and wheel spin occurrence for specified values of input parameters including engine torque vs. rpm, transmission and final drive ratios, weight, weight distribution, lift coefficient, drag coefficient, frontal area, air density, and salt/tire static friction coefficient. A typical result is shown in the above graph for a vehicle weight of 800 lbs, drag coefficient 0.15, frontal area 5 square feet, final drive ratio 1.79, and friction coefficient 0.6. A 600 cc sport bike engine produces about 113 crank horsepower at 14,000 rpm at standard sea level conditions. However, temperature, humidity, and altitude at at Bonneville reduce the air density, and thus the power, by a factor of about 0.79, and there are also drive line losses. I expect the 600 cc 4-stroke engine peak power at the rear wheel to be about 85 horsepower at Bonneville. The graph shows that average top speed in the fifth mile could be as high as about 245 mph.

There is theoretically no difference between theory and experiment. 

This is a specialized "curve fit" of speed records for naturally aspirated gas streamliners.


Another way to estimate achievable top speed, and to check the accuracy of the computer model results, is to curve fit speed record data. I plotted motorcycle speed records for the complete displacement range of naturally aspirated gas engine streamliners, and drew a line that passes through a few of the highest record speeds. This establishes a reasonable maximum speed expectation for any displacement class. This is not a “best fit” to all of the data, but rather a line that passes through the three or four highest class record speeds that have been achieved across the engine displacement spectrum. It does not represent the maximum possible, but does represent a reasonably attainable and quite admirable performance plateau. This procedure suggests that a speed of 243 mph should be reasonably achievable for a 650 cc streamliner, given a sufficiently powerful engine in a state of engine tune that has been attained by record holders, a well-designed low-drag vehicle, a qualified rider, and favorable conditions. This estimate agrees remarkably well with the detailed analysis results (245 mph) presented above. A 1000 cc engine bumps the top speed up to 280 mph, while 157 mph should be possible with a 175 cc engine, and 103 mph (which has recently been exceeded by a considerable margin) for a 50 cc engine. This analysis could be done for any engine and frame classifications combination.

The physics basis for this procedure is as follows. Maximum speed occurs when the available power is equal to the product of speed and the net force that must be overcome, which is essentially the sum total of aerodynamic drag and rolling resistance, both of which are roughly proportional to speed squared. The power required to maintain a given speed is therefore approximately proportional to the cube of speed, or, inversely, achievable speed is approximately proportional to the cube root of available power. That means that doubling power will increase speed by about 25%. The maximum power available from an engine is (very) roughly proportional to engine displacement for a given engine configuration and state of tune. A highly approximate, but workable, curve fit equation is    speed = constant x displacement ^ (1/3).    I replaced the exponent “1/3” by an exponent of unknown value to allow a better fit of the empirical speed data. This equation glosses over many details such as how rolling and aerodynamic resistance and engine power vary during a run, and the effect of many engine characteristics such as engine design, cylinder size, number of cylinders, Brake Mean Effective Pressure (BMEP), and state of tune. All of these considerations affect the value of the constants and exponents in, and the accuracy and reliability of, this approximate equation. This analysis provides no information regarding the optimum overall drive ratio or shift points or value of any operational parameter, but does serve as a valuable check on the validity of results of computerized performance modeling. 

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