(U.S. Patent 4,603,582)
Horsepower = Torque x RPM / 5252
There are two basic types of brake dynamometers; the Engine Dynamometer which takes power directly from the output shaft of the engine and the Chassis Dynamometer which takes power from the drive wheels of the vehicle. Although these dynamometers are the most commonly used test equipment for the determination of automotive engine horsepower, they have several drawbacks as follows:
Cost is also a considerable factor with the above dynamometers. Basic units start at many thousands of dollars. Additionally, they often require support systems such as a test cell, control console, large water supply, exhaust systems, and large air circulation system. The use of these dynamometers is therefore generally limited to the automotive professional or serious auto racer.
Another method whereby the horsepower of an automotive engine may be determined is to employ a torque sensor in the vehicle of the engine under test. This sensor may be of the type that is installed in series with the drive train of the vehicle or it may take on the form of a sensor that detects the rotation of the engine against its mounts. The torque and RPM are measured and the horsepower is calculated in the same manner as the brake dynamometer This method does not require support systems and has the advantage of being able to determine engine horsepower while driving the vehicle on the road or track. The disadvantage is that a torque sensor with any degree of accuracy is generally very expensive and difficult to implement.
A significant shortcoming of both brake dynamometers and in-vehicle torque sensor methods is that they determine the output horsepower of the engine only. They are not capable of measuring other vehicular parameters such as the horsepower dissipated by frictional, viscous, or aerodynamic drag.
The amount of horsepower lost to drag can become quite large with some vehicles, even at very low speeds. High amounts of drag due to friction may indicate a vehicular malfunction. Excessive drag causes a proportionate loss of fuel economy. Aerodynamic drag becomes the limiting factor when it comes to the top speed of a racing vehicle. Because of these facts, it is very desirable to be able to measure the amount of horsepower lost to vehicular drag as well as the engine horsepower to determine overall vehicular performance.
To put things into perspective, lets return to Watt's definition of Horsepower. He said that a work horse of his time could lift a 550 pound weight one foot in one second, See Figure 1. With a little math we can convert Watt’s definition into terms that make more sense in the automotive field. If the time required to lift the weight is increased to one hour (3600 seconds), the amount of weight that can be lifted by one horsepower will increased by 3600 to 1. Therefore one horsepower can lift 1,980,000 pounds one foot in one hour. Now if the lift distance is increased to one mile (5280 feet), the amount weight one horsepower will lift will be reduced by 5280 to 1 for a new weight of 375 pounds. The definition of horsepower in automotive terms is therefore the power required to lift 375 pounds one mile in one hour.
Now referring to Figure 2, imagine that the 375 pound weight is actually a 375 pound automobile and the source of power is the engine of the vehicle. For the time being, the vehicle will be shown on a hill that goes straight up and the assumption will be made that the drive wheels will be able to maintain traction under these conditions. If the hand brake is set, the full 375 pound weight of the vehicle will be applied to the ground by the drive wheels of the vehicle. To put it another way, the drive wheels will be applying a force of 375 pounds to the ground just to keep the vehicle from rolling backwards. Assume now that vehicle has a automatic transmission and the engine is used to hold the vehicle at a standstill on the hill. The force being applied to ground will be 375 pounds. The amount of power being applied to the ground however will be zero as the vehicle is not moving and no work is being done. The engine is actually putting out power but it is being dissipated in the form of heat by the torque converter of the transmission. If the engine is given more throttle, a force of greater than 375 pounds will be applied to the ground and the vehicle will begin to move upward. If the vehicle is allowed to reach one mile per hour and then held at that speed, the force will return to a steady 375 pounds. With the vehicle now moving up the hill at one mile per hour and the drive wheels applying a force to the ground of 375 pounds, it can be shown through the use of the automotive definition of horsepower that one horsepower is being applied to the ground. If the speed is doubled the horsepower will be doubled. It now appears that all that needs to be done to determine how much horsepower is being applied to the ground, is to measure the force being applied to the ground, measure the vehicle speed, multiply the force times speed, and divide by 375. Thus:
Horsepower = Force x Speed / 375
The measurement of vehicle speed is a simple matter of monitoring the output of a speed transducer that is located in the speedometer system of the vehicle. The determination of the amount of drive wheel force is a little more complicated and is resolved by the use of a device that is commonly used by the aerospace and inertial guidance industry. This device is called a accelerometer and it is used to measure acceleration.
Assume now that the vehicle of Figure 2 has both a speed transducer and accelerometer whose sensitive axis is parallel to the surface of the road and pointed in the direction of travel. With the accelerometer mounted in this manner, it will be sensitive to acceleration in the fore/aft direction only. The speed transducer will measure the speed of the vehicle while the accelerometer will measure the acceleration of the vehicle in g units (Gravity Units). As the vehicle is pointed straight up, the output from the accelerometer will be 1.0g due to the pull of gravity if the vehicle is standing still or traveling at a steady speed. If the vehicle is increasing or decreasing in speed, the accelerometer will sense more or less than 1.0g as the vehicle acceleration will be adding or subtracting from the gravitational pull of 1.0g. (Note: There is no way that a human or an accelerometer can tell the difference between acceleration due to gravity or acceleration due to vehicular acceleration.
Another law from physics states that Force = Mass x Acceleration. For the purpose of this discussion, the term Mass will be replaced with Weight. Therefore, Force = Weight x Acceleration. It can be shown from this law that all that is necessary to determine the force at the drive wheels of the vehicle is to multiply the Weight of the vehicle times the Acceleration. From this it can be seen that a new horsepower formula may be derived by rewriting the above formula in the following manner:
Horsepower = Force x Speed /
With this new formula it can now be seen that one only need to know the vehicle weight, acceleration, and speed to determine horsepower ---- all without connecting anything to the engine itself. This can be confirmed with the vehicle of Figure 2 that is moving up hill at one mile per hour under 1.0 g of acceleration:
375 x 1 x 1 / 375 = 1 Horsepower
The Inertial Dynamometer:
Consider now the vehicle of Figure 3. Note that this vehicle is shown traveling along level ground and the weight is now a more realistic 3750 pounds. Assume that the vehicle is equipped with the same speed transducer and accelerometer arrangement as the vehicle of Figure 2. If the vehicle were to be accelerated, the accelerometer would sense the acceleration just as though it were being caused by the pull of gravity. The contribution due to the pull of gravity however will be zero as the sensitive axis of the accelerometer is now at a right angle to the pull of gravity. Therefore the acceleration that will sensed will be that of the actual acceleration of the vehicle.
As it was shown in Figure 2 that the gravitational pull of 1.0g would cause a force equal to the weight of the vehicle to be applied to the ground by the drive wheels of the vehicle, it can also be shown in Figure 3 that a force equal to the weight of the vehicle being applied to the ground by the drive wheels of the vehicle will cause a vehicular acceleration of 1.0g. This can be confirmed by rewriting the force formula in the following manner:
Force = Weight x Acceleration
Using this new formula it can be shown that if the drive wheels of the vehicle of Figure 3 were to apply a force of 3750 pounds to the ground, the vehicle would accelerate at a rate of 1.0g. This exercise illustrates the fact that the accelerometer is sensitive only to the acceleration caused by the force being applied to the ground by the drive wheels of the vehicle and it does not matter whether the vehicle is on level ground or a hill when measurements are being made. This same exercise may also be used to show that the accelerometer is sensitive only to the deceleration caused by the force of vehicular drag acting against the vehicle when it is allowed to coast in neutral and is again not affected by hills. Vehicular drag will be discussed in greater detail later.
Imagine now that the vehicle of Figure 3 is accelerating from a standstill to 50 MPH. As the vehicle continues to accelerate, the computer using a vehicular weight of 3750 pounds, will continuously monitor the acceleration and speed of the vehicle and calculate the value of horsepower. As an example, suppose that the acceleration is .750 g at 30 MPH. The computer will use these values to compute horsepower in the following manner:
Weight x Acceleration x Speed / 375
If upon reaching 50 MPH, the power is reduced to the point that the vehicle will be cruising steadily, the acceleration will drop to zero and the indication of horsepower will be zero. This may not seem quite right to some as we all know it takes power to cruise an automobile on level ground. What is actually being measured is Net Horsepower. Net Horsepower is defined as the power being applied to the ground by the drive wheels of the vehicle that is in excess of the amount required to overcome vehicular drag. This vehicular drag is the result of the combined effects of frictional, viscous and aerodynamic drag of the vehicle. Net Horsepower may also be looked upon as the excess power available to accelerate the vehicle.
The total horsepower being applied to the ground by the drive wheels of the vehicle is referred to as Gross Horsepower. It is defined as the sum of the power required to accelerate the vehicle and the power required to overcome vehicular drag. The measurement of Gross Horsepower requires more computational steps by the computer as will be described below.
If the computer is to determine the amount of Gross Horsepower, it must first determine the drag characteristics of the vehicle at all speeds within the operating range of the vehicle. The computer may then use this knowledge of vehicular drag during the measurement and computation of Gross Horsepower. The problem of determining the drag characteristics at all speeds is simplified by the fact that the drag characteristics of an automobile are highly predictable with the knowledge of a single low speed drag value and a single high speed drag value.
Although vehicular drag characteristics vary greatly between different types of vehicles, it has been found that the modern mid-sized automobile will more or less decelerate with the following characteristics when allowed to coast in neutral:
Deceleration due to frictional drag is approximately: .015g at all speeds.
Deceleration due to viscous drag is approximately: .0001g x MPH.
Deceleration due to aerodynamic drag is approximately: .000005 g x MPH2
From the above it can be shown that if the deceleration values are known for each of the drag characteristics at a given speed, they can be calculated for any other speed. It is then a simple matter of adding together all of these deceleration values for a total deceleration value at said speed. As the total deceleration is equal to the amount of additional acceleration the vehicle would have if it had zero vehicular drag, it is only necessary to add this deceleration to the acceleration of the Net Horsepower formula to create a new formula for the determination of Gross Horsepower. Thus:
Net Horsepower = Weight x Acceleration x Speed
Assume now that the computer on board the vehicle of Figure 3 is the computer of the DynoLab On-Board Dyno and it is operating in the Gross Horsepower mode. In order to make accurate measurements of Gross Horsepower, the computer must first determine the drag characteristics of the vehicle and this is done in the following manner:
(1) The vehicle is first allowed to coast in neutral at a speed of less than 10 MPH. At low speeds the aerodynamic and viscous drag on the vehicle will be almost nonexistent and the deceleration of the vehicle will be the result of the frictional drag on the vehicle. The value of deceleration is established as the frictional drag constant and is stored in the memory of the On-Board Dyno.
(2) The viscous drag on the vehicle is considered to be insignificant except at very high speeds or for very heavy vehicles. Therefore a viscous drag constant value of .0001g at one mile per hour is permanently stored in the memory of the On-Board Dyno.
(3) The vehicle is allowed to coast in neutral at a speed that is greater than 50 MPH. The deceleration and speed of the vehicle are then measured by the computer. At high speeds the deceleration of the vehicle will be the results of the combined effects of frictional, viscous, and aerodynamic drag. In order to determine a deceleration value for aerodynamic drag only, the computer of the On-Board Dyno must first calculate the values of frictional and viscous drag at the speed which the high speed measurement was made. These values are then subtracted from the total deceleration at that speed. The computer then, using the remaining deceleration value and the speed at which it was determined, calculates an aerodynamic drag constant for the vehicle at one mile per hour. This value is then stored in the memory of the On-Board Dyno.
Once the drag characteristics of the vehicle are determined and converted to drag constants at one mile per hour, the On-Board Dyno will be ready to calculate the total deceleration due to vehicular drag at any other speed.
As an example, suppose the vehicle of Figure 3 is traveling at 65 MPH and it has the drag characteristics of the modern mid-sized automobile described above. The computer will calculate the total deceleration due to vehicular drag in the following manner:
.015 + (.0001 x 65) + (.000005 x 652) = .043g
The On-Board Dyno may now use this deceleration value during the computation of Gross Horsepower. As the vehicle is traveling at a steady 65 MPH on level ground, the accelerometer will sense zero g and the computer will, using the Gross formula, calculate the Gross Horsepower as follows:
3750 x (0 + .043) x 65 / 375 = 28 Gross Horsepower
This 28 horsepower is the total power being applied to the ground by the drive wheels of the vehicle and is equal to the amount of power required to overcome vehicular drag at 65 MPH. If the On-Board Dyno were to be switched to the Net mode and the vehicle allowed to coast in neutral at 65 MPH, the accelerometer would sense a deceleration of -.043g. The computer would then, using the Net Horsepower formula, calculate the amount of horsepower being consumed by vehicular drag. Thus:
3750 x -.043 x 65 / 375 = -28 Net Horsepower
As a second example of the measurement of Gross Horsepower, suppose that the vehicle is under acceleration of .500g at 65 MPH. The Gross horsepower being applied to the ground by the drive wheels of the vehicle will be calculated in the following manner:
3750 x (.500 + .043) x 65 / 375 = 353 Gross Horsepower
Of this 353 horsepower, 28 are used to overcome vehicular drag while the remaining 325 horsepower are used to accelerate the vehicle.
The Real World:
With regard to the weight of the vehicle, it was assumed that the weight of the vehicle was the only weight that needed to be considered. The total weight of the vehicle should in fact include the weight of the driver, passengers, and any additional weight that might be carried on board. Also, when the vehicle is under acceleration, the increase in rotational speed of each tire, wheel, and brake rotor or drum should be considered. The rotational acceleration of these components tends to resist the acceleration of the vehicle and makes the vehicle seem heavier than it's measured weight. Bulletin J1263 from the S.A.E. states that a value of 3 percent may be used to estimate the effective increase in vehicular weight due to these components. The On- Board Dyno allows the user input this value of rotational mass. Other values may be entered if non-stock wheels and tires are being used.
Although it was stated in the above discussion that the speed transducer would measure the vehicle speed in miles per hour, the output of the transducer is actually a series of pulses and the number of pulses per mile varies from one automobile manufacture to another. For this reason it will be necessary to calibrate the On-Board Dyno with respect to the speedometer system of the vehicle in which it is being used. If the number of pulses per mile is known at the time of calibration, it may be entered directly. If the number of pulses per mile is not known, the value may be entered automatically by driving the vehicle through a measured mile. (Miles markers may be found on most state roads and freeways.)
During the discussion of the vehicle of Figure 3 it was stated that the sensitive axis of the accelerometer was at a right angle to the roadway surface. This is not always true as most automotive type vehicles will pitch-up while under acceleration due to the springs of their suspensions systems. This pitch-up will cause the accelerometer to sense an additional acceleration, albeit very small, due to the pull of gravity. This additional acceleration will make the accelerometer appear to be overly sensitive. The On-Board Dyno provides the operator with a method of compensating for the vehicle pitch-up. During the vehicular calibration of the On-Board Dyno to the vehicle in which it is being used, the operator will be asked to input an appropriate pitch-up angle in degrees for the vehicle. The table below is a listing of typical pitch-up angles for several types of vehicles.
Suspension Vehicle Type Angle Rigid No springs 0.0 Hard Dragster 0.5 Semi Hard Race Car 1.0 Medium Production Sports Car 1.5 Soft Production Sedan 2.0 Very Soft Early Production Sedan 2.5 Trick Super Lift 3.0
During the measurement of horsepower it will not be unusual to note a significant difference in power between the lowest and highest gears of the vehicle. The reasons for this is that the engine must not only accelerate the vehicle but it must also accelerate the speed of the engine flywheel, crankshaft, connecting rods, pistons, and etc. The inertia of these components tends to resist an increase of engine RPM. The effect will be most pronounced in low gear as RPM increases most rapidly in this gear and the inertia of the components will have the greatest tendency to resist the increase. There will also be an apparent loss or gain of horsepower when the vehicle is accelerating down hill or up hill. When the vehicle is going down hill, the engine will gain RPM more rapidly and the inertia of the engine components will cause a greater loss than if the vehicle were accelerating up hill. The loss of horsepower due to the inertia of the engine components is real and it illustrates the desirability of lighter engine components in high performance engines.
Gross Horsepower In this mode the total horsepower being applied to the ground by the drive wheels of the vehicle may be determined. The value of Gross Horsepower indicated by the On- Board Dyno will be nearly that of the actual output of the engine. The drive train losses of most vehicles are lower than one might expect and a good portion of these losses are accounted for during calibration of the instrument to the vehicle in which it is being used. If the vehicle is allowed to coast in neutral, the indication will be zero. If the brakes are applied, the indication will be that of the power dissipated by the brakes. If the vehicle is allowed to coast while in gear, the indication will be that of the frictional losses of the engine and drive train.
Net Horsepower This mode is typically used to measure the horsepower dissipated by vehicular drag. If the vehicle is allowed to coast in neutral, the indication will that of the horsepower lost to the combined affects of frictional, viscous, and aerodynamic drag. Any changes of vehicular drag will be noted quickly in this mode.
Acceleration While in this mode the acceleration or deceleration of the vehicle may be measured. It is useful for optimizing such traction controlling items as tires, tire pressure, and suspension systems. Acceleration controlling items such as gear ratios, clutches, and proper RPM for leaving the line can also be optimized by monitoring acceleration. The deceleration caused by the brakes of the vehicle is an indication of the efficiency of the brakes. The deceleration of the vehicle when allowed to coast in neutral is the result of the combined effects of frictional, viscous, and aerodynamic drag. The force of this vehicular drag may be calculated by multiplying the deceleration times the weight of the vehicle.
Speed While in the speed mode, the indication will that of the speed of the vehicle in miles per hour. If the measured mile method is used during the calibration of the On-Board Dyno to the vehicle in which it is being used, the indications will be extremely accurate as most states do a very good job of placing the mile markers. The indications may be then used to check the accuracy of the vehicle speedometer.
Peak Reading During the normal operation of the On-Board Dyno, the peak values of Horsepower, Acceleration, and Speed will be detected and stored in memory. These values may be recalled at any time.
Vehicular Drag The drag characteristics of the vehicle are stored in memory during calibration of the On-Board Dyno to the vehicle in which it is being used. Of these, the frictional and aerodynamic drag constants may be recalled and displayed.
The display of the frictional drag constant will be that of the number of pounds of frictional drag per pound of vehicle weight while coasting in neutral. The frictional drag constant will also represent the deceleration of the vehicle in milli gs, due to frictional drag while coasting in neutral. A typical value of .015 pounds per pound or .015g will be displayed as 15.0.
The display of the aerodynamic drag constant will be that of the number of pounds of aerodynamic drag per pound of vehicle weight while coasting in neutral at one mile per hour. The aerodynamic drag constant will also represent the deceleration of the vehicle in micro gs due to the aerodynamic drag while coasting in neutral at one mile per hour. A typical value of .000005 pounds per pound or .000005g would be displayed as 5.0.
If the drag calibration procedure is repeated occasionally and the constants are recalled, the drag characteristics of the vehicle may be monitored for any changes that might occur. As an example, an increase of the frictional drag constant from 15.0 to 30.0 may indicate that the brakes are dragging or a tire may be low.
The aerodynamic value is not likely to change unless modifications are made to the vehicle or the ride attitude changes. The aerodynamic drag constant may however be used to calculate the aerodynamic drag coefficient of the vehicle if the projected frontal area is known. The formula for the calculation is as follows:
Cd = Ca x W / 2560 x A
Where: Cd = Aerodynamic Drag Coefficient Ca = Aerodynamic Drag Constant W = Weight of the vehicle [pounds] A = Projected Frontal Area [square feet]
Cd = (5.00 x 3750) / 2560 x 20 = .366
The aerodynamic pressure against the vehicle may also be determined by using the following formula:
Ap = Ca x MPH2 x W / 1,000,000
Where Ap = Aerodynamic Pressure
Ap = 5.00 x 1502 x 3750 / 1,000,000 = 422 Lbs
(U.S. Patent 4,603,582)