# Dynamometer

Template:Refimprove
For the dynamometer used in railroading, see dynamometer car.
Early hydraulic dynamometer, with dead-weight torque measurement.

A dynamometer or "dyno" for short, is a device for measuring force, moment of force (torque), or power. For example, the power produced by an engine, motor or other rotating prime mover can be calculated by simultaneously measuring torque and rotational speed (RPM).

A dynamometer can also be used to determine the torque and power required to operate a driven machine such as a pump. In that case, a motoring or driving dynamometer is used. A dynamometer that is designed to be driven is called an absorption or passive dynamometer. A dynamometer that can either drive or absorb is called a universal or active dynamometer.

In addition to being used to determine the torque or power characteristics of a machine under test (MUT), dynamometers are employed in a number of other roles. In standard emissions testing cycles such as those defined by the US Environmental Protection Agency (US EPA), dynamometers are used to provide simulated road loading of either the engine (using an engine dynamometer) or full powertrain (using a chassis dynamometer). In fact, beyond simple power and torque measurements, dynamometers can be used as part of a testbed for a variety of engine development activities such as the calibration of engine management controllers, detailed investigations into combustion behavior and tribology.

In the medical terminology, hand-held dynamometers are used for routine screening of grip and hand strength and initial and ongoing evaluation of patients with hand trauma or dysfunction. They are also used to measure grip strength in patients where compromise of the cervical nerve roots or peripheral nerves is suspected.

In the rehabilitation, kinesiology, and ergonomics realms, force dynamometers are used for measuring the back, grip, arm, and/or leg strength of athletes, patients, and workers to evaluate physical status, performance, and task demands. Typically the force applied to a lever or through a cable are measured and then converted to a moment of force by multiplying by the perpendicular distance from the force to the axis of the level.[1]

## Principles of operation of torque power (absorbing) dynamometers

An absorbing dynamometer acts as a load that is driven by the prime mover that is under test (e.g. Pelton wheel). The dynamometer must be able to operate at any speed and load to any level of torque that the test requires.

Absorbing dynamometers are not to be confused with "inertia" dynamometers, which calculate power solely by measuring power required to accelerate a known mass drive roller and provide no variable load to the prime mover.

An Absorption dynamometer is usually equipped with some means of measuring the operating torque and speed.

The dynamometer's Power Absorption Unit absorbs the power developed by the prime mover. The power absorbed by the dynamometer is converted into heat and the heat generally dissipates into the ambient air or transfers to cooling water that dissipates into the air. Regenerative dynamometers, in which the prime mover drives a DC motor as a generator to create load, make excess DC power and potentially, using a DC/AC inverter, can feed AC power back into the commercial electrical power grid - where the power produced is eventually converted back into heat (as in an oven or light bulb, etc.).

Absorption dynamometers can be equipped with two types of control systems to provide different main test types.

Constant Force
The dynamometer has a "braking" torque regulator, the PAU (Power Absorption Unit) is configured to provide a set braking force torque load while the prime mover is configured to operate at whatever throttle opening, fuel delivery rate or any other variable it is desired to test. The prime mover is then allowed to accelerate the engine through the desired speed or RPM range. Constant Force test routines require the PAU to be set slightly torque deficient as referenced to prime mover output to allow some rate of acceleration. Power is calculated based on rotational speed x torque x constant. The constant varies depending on the units used.

Constant Speed
If the dynamometer has a speed regulator (human or computer), the PAU provides a variable amount of braking force (torque) that is necessary to cause the prime mover to operate at the desired single test speed or RPM. The PAU braking load applied to the prime mover can be manually controlled or determined by a computer. Most systems employ eddy current, oil hydraulic or DC motor produced loads because of their linear and quick load change ability.

Power is calculated based on rotational speed x torque x constant, constant varies depending on output unit desired and input units used.

A motoring dynamometer acts as a motor that drives the equipment under test. It must be able to drive the equipment at any speed and develop any level of torque that the test requires. In common usage, AC or DC motors are used to drive the equipment or "load" device.

In most dynamometers power (P) is not measured directly; it must be calculated from torque (τ) and angular velocity (ω)Template:Citation needed values or force (F) and linear velocity (v):

$P=\tau\cdot\omega$
or
$P=F \cdot v$
where
P is the power in watts
τ is the torque in newton metres
ω is the angular velocity in radians per second
F is the force in newtons
v is the linear velocity in metres per second

Division by a conversion constant may be required depending on the units of measure used.

For imperial units,

$P_\mathrm{hp}={\tau_\mathrm{lb \cdot ft}\cdot\omega_\mathrm{rpm} \over 5252}$
where
Php is the power in horsepower
τlb·ft is the torque in pound-feet
ωRPM is the rotational velocity in revolutions per minute

For metric units,

$P_\mathrm{kW}={\tau_\mathrm{N \cdot m}\cdot\omega_\mathrm{rpm} \over 9549}$
where
PkW is the power in kilowatts
τN·m is the torque in newton metres
ωrpm is the rotational velocity in revolutions per minute

## Detailed dynamometer description

Electrical dynamometer setup showing engine, torque measurement arrangement and tachometer

A dynamometer consists of an absorption (or absorber/driver) unit, and usually includes a means for measuring torque and rotational speed. An absorption unit consists of some type of rotor in a housing. The rotor is coupled to the engine or other equipment under test and is free to rotate at whatever speed is required for the test. Some means is provided to develop a braking torque between dynamometer's rotor and housing. The means for developing torque can be frictional, hydraulic, electromagnetic etc. according to the type of absorption/driver unit.

One means for measuring torque is to mount the dynamometer housing so that it is free to turn except that it is restrained by a torque arm. The housing can be made free to rotate by using trunnions connected to each end of the housing to support the dyno in pedestal mounted trunnion bearings. The torque arm is connected to the dyno housing and a weighing scale is positioned so that it measures the force exerted by the dyno housing in attempting to rotate. The torque is the force indicated by the scales multiplied by the length of the torque arm measured from the center of the dynamometer. A load cell transducer can be substituted for the scales in order to provide an electrical signal that is proportional to torque.

Another means for measuring torque is to connect the engine to the dynamometer through a torque sensing coupling or torque transducer. A torque transducer provides an electrical signal that is proportional to torque.

With electrical absorption units, it is possible to determine torque by measuring the current drawn (or generated) by the absorber/driver. This is generally a less accurate method and not much practiced in modern times, but it may be adequate for some purposes.

When torque and speed signals are available, test data can be transmitted to a data acquisition system rather than being recorded manually. Speed and torque signals can also be recorded by a chart recorder or plotter.

## Types of dynamometers

In addition to classification as Absorption, Motoring or Universal as described above, dynamometers can be classified in other ways.

A dyno that is coupled directly to an engine is known as an engine dyno.

A dyno that can measure torque and power delivered by the power train of a vehicle directly from the drive wheel or wheels (without removing the engine from the frame of the vehicle), is known as a chassis dyno.

Dynamometers can also be classified by the type of absorption unit or absorber/driver that they use. Some units that are capable of absorption only can be combined with a motor to construct an absorber/driver or universal dynamometer. The following types of absorption/driver units have been used:

### Eddy current type absorber

EC dynamometers are currently the most common absorbers used in modern chassis dynos. The EC absorbers provide the quick load change rate for rapid load settling. Most are air cooled, but some are designed to require external water cooling systems.

Eddy current dynamometers require an electrically conductive core, shaft or disc, moving across a magnetic field to produce resistance to movement. Iron is a common material, but copper, aluminum and other conductive materials are usable.

In current (2009) applications, most EC brakes use cast iron discs, similar to vehicle disc brake rotors, and use variable electromagnets to change the magnetic field strength to control the amount of braking.

The electromagnet voltage is usually controlled by a computer, using changes in the magnetic field to match the power output being applied.

Sophisticated EC systems allow steady state and controlled acceleration rate operation.

### Powder dynamometer

A powder dynamometer is similar to an eddy current dynamometer, but a fine magnetic powder is placed in the air gap between the rotor and the coil. The resulting flux lines create "chains" of metal particulate that are constantly built and broken apart during rotation creating great torque. Powder dynamometers are typically limited to lower RPM due to heat dissipation issues.

### Hysteresis dynamometers

Hysteresis dynamometers, use a steel rotor that is moved through flux lines generated between magnetic pole pieces. This design, as in the usual "disc type" eddy current absorbers, allows for full torque to be produced at zero speed, as well as at full speed. Heat dissipation is assisted by forced air. Hysteresis and "disc type" EC dynamometers are one of the most efficient technologies in small (200 hp (150 kW) and less) dynamometers. A hysteresis brake is an eddy current absorber that, unlike most "disc type" eddy current absorbers, puts the electromagnet coils inside a vented and ribbed cylinder and rotates the cylinder, instead of rotating a disc between electromagnets. The potential benefit for the hysteresis absorber is that the diameter can be decreased and operating RPM of the absorber may be increased.

### Electric motor/generator dynamometer

Electric motor/generator dynamometers are a specialized type of adjustable-speed drives. The absorption/driver unit can be either an alternating current (AC) motor or a direct current (DC) motor. Either an AC motor or a DC motor can operate as a generator that is driven by the unit under test or a motor that drives the unit under test. When equipped with appropriate control units, electric motor/generator dynamometers can be configured as universal dynamometers. The control unit for an AC motor is a variable-frequency drive and the control unit for a DC motor is a DC drive. In both cases, regenerative control units can transfer power from the unit under test to the electric utility. Where permitted, the operator of the dynamometer can receive payment (or credit) from the utility for the returned power via net metering.

In engine testing, universal dynamometers can not only absorb the power of the engine, but also drive the engine for measuring friction, pumping losses and other factors.

Electric motor/generator dynamometers are generally more costly and complex than other types of dynamometers.

### Fan brake

A fan is used to blow air to provide engine load. The torque absorbed by a fan brake may be adjusted by changing the gearing or the fan itself, or by restricting the airflow through the fan. It should be noted that, due to the low viscosity of air, this variety of dynamometer is inherently limited in the amount of torque that it can absorb.

### Hydraulic brake

The hydraulic brake system consists of a hydraulic pump (usually a gear type pump), a fluid reservoir and piping between the two parts. Inserted in the piping is an adjustable valve and between the pump and the valve is a gauge or other means of measuring hydraulic pressure. In simplest terms, the engine is brought up to the desired RPM and the valve is incrementally closed and as the pump's outlet is restricted, the load increases and the throttle is simply opened until at the desired throttle opening. Unlike most other systems, power is calculated by factoring flow volume (calculated from pump design specs), hydraulic pressure and RPM. Brake HP, whether figured with pressure, volume and RPM or with a different load cell type brake dyno, should produce essentially identical power figures. Hydraulic dynos are renowned for having the absolute quickest load change ability, just slightly surpassing the eddy current absorbers. The downside is that they require large quantities of hot oil under high pressure and the requirement for an oil reservoir.

### Water brake type absorber

The water brake absorber is sometimes mistakenly called a "hydraulic dynamometer." Water brake absorbers are relatively common, having been manufactured for many years and noted for their high power capability, small package, light weight, and relatively low manufacturing cost as compared to other, quicker reacting "power absorber" types.

Their drawbacks are that they can take a relatively long period of time to "stabilize" their load amount and the fact that they require a constant supply of water to the "water brake housing" for cooling. In many parts of the countryTemplate:Fix, environmental regulations now prohibit "flow through" water and large water tanks must be installed to prevent contaminated water from entering the environment.

The schematic shows the most common type of water brake, the variable level type. Water is added until the engine is held at a steady RPM against the load. Water is then kept at that level and replaced by constant draining and refilling, which is needed to carry away the heat created by absorbing the horsepower. The housing attempts to rotate in response to the torque produced but is restrained by the scale or torque metering cell that measures the torque.
This schematic shows a water brake, which is actually a fluid coupling with a housing restrained from rotating—similar to a water pump with no outlet.

### Compound Dynamometers

In most cases, motoring dynamometers are symmetrical; a 300 kW AC dynamometer can absorb 300 kW as well as motor at 300 kW. This is an uncommon requirement in engine testing and development. Sometimes, a more cost-effective solution is to attach a larger absorption dynamometer with a smaller motoring dynamometer; alternatively, a larger absorption dynamometer and a simple AC or DC motor may be used in a similar manner with the electric motor only providing motoring power when required and no absorption. The (cheaper) absorption dynamometer is sized for the maximum required absorption, whereas the motoring dynamometer is sized for motoring. A typical size ratio for common emission test cycles and most engine development is approximately 3:1. Torque measurement is somewhat complicated since there are two machines in tandem; an inline torque transducer is the preferred method of torque measurement in this case. An eddy-current or waterbrake dynamometer with electronic control combined with a variable frequency drive and AC induction motor is a commonly used configuration of this type. Disadvantages include requiring a second set of test cell services (electrical power and cooling), and a slightly more complicated control system. Attention must be paid to the transition between motoring and braking in terms of control stability.

## How dynamometers are used for engine testing

Dynamometers are useful in the development and refinement of modern day engine technology. The concept is to use a dyno to measure and compare power transfer at different points on a vehicle, thus allowing the engine or drivetrain to be modified to get more efficient power transfer. For example, if an engine dyno shows that a particular engine achieves 400 N·m (300 lbf·ft) of torque, and a chassis dynamo shows only 350 N·m (260 lbf·ft), one would know to look to the drivetrain for the major improvements. Dynamometers are typically very expensive pieces of equipment, reserved for certain fields that rely on them for a particular purpose.

## Types of dynamometer systems

Dyno graph 1
Dyno graph 2

A brake dynamometer applies variable load on the Prime Mover (PM) and measures the PM's ability to move or hold the RPM as related to the "braking force" applied. It is usually connected to a computer that records applied braking torque and calculates engine power output based on information from a "load cell" or "strain gauge" and RPM (speed sensor).

An inertia dynamometer provides a fixed inertial mass load and calculates the power required to accelerate that fixed, known mass and uses a computer to record RPM and acceleration rate to calculate torque. The engine is generally tested from somewhat above idle to its maximum RPM and the output is measured and plotted on a graph.

A motoring dynamometer provides the features of a brake dyne system, but in addition, can "power" (usually with an AC or DC motor) the Prime Mover (PM) and allow testing of very small power small outputs. Example, duplicating speeds and loads that are experienced when operating a vehicle traveling downhill or on/off throttle operations.

### There are essentially 3 types of dynamometer test procedures

1. Steady state (only on brake dynamometers), where the engine is held at a specified RPM (or series of usually sequential RPMs) for a desired amount of time by the variable brake loading as provided by the PAU (power absorber unit)
2. Sweep test (on inertia or brake dynamometers), where the engine is tested under a load (inertia or brake loading), but allowed to "sweep" up in RPM in a continuous fashion, from a specified lower "starting" RPM to a specified "end" RPM
3. Transient test (usually on AC or DC dynamometers), where the engine power and speed are varied throughout the test cycle. Different test cycles are used in different jurisdictions. Chassis test cycles include the US light-duty UDDS, HWFET, US06, SC03, ECE, EUDC, and CD34. Engine test cycles include ETC, HDDTC, HDGTC, WHTC, WHSC, and ED12.

Types of Sweep Tests:

1. Inertia sweep: An inertia dyno system provides a fixed inertial mass flywheel and computes the power required to accelerate the flywheel (load) from the starting to the ending RPM. The actual rotational mass of the engine or engine and vehicle in the case of a chassis dyno is not known and the variability of even tire mass will skew power results. The inertia value of the flywheel is "fixed," so low power engines are under load for a much longer time and internal engine temperatures are usually too high by the end of the test, skewing optimal "dyno" tuning settings away from the outside world's optimal tuning settings. Conversely, high powered engines, commonly complete a common "4th gear sweep" test in less than 10 seconds, which is not a reliable load condition as compared to operation in the outside world. By not providing enough time under load, internal combustion chamber temps are unrealistically low and power readings, especially past the power peak, are skewed low.
1. Loaded Sweep Tests (brake dyno type) consist of 2 types:
1. Simple fixed Load Sweep Test: A fixed load, of somewhat less than the engine's output, is applied during the test. The engine is allowed to accelerate from its starting RPM to its ending RPM, varying in its own acceleration rate, depending on power output at any particular rotational speed point. Power is calculated using rotational speed x torque x constant + the power required to accelerate the dyno and engine's / vehicle's rotating mass.
2. Controlled Acceleration Sweep Test: Similar in basic usage as the above Simple fixed Load Sweep Test, but with the addition of active load control that targets a specific rate of acceleration. Commonly, 20fps/ps is usedTemplate:Citation needed

Controlled Acceleration Rate test is that the acc. rate used is controlled from low power to high power engines and over extension and contraction of "test duration" is avoided, providing more repeatable tests and tuning results.

In every Sweep Test, there is still the remaining issue of potential power reading error due to the variable engine / dyno / vehicle total rotating mass. Many modern computer controlled brake dyno systems are capable of deriving that "inertial mass" value to eliminate the error.Template:Fix

Interestingly, A "sweep test" will always be suspect, as many "sweep" users ignore the rotating mass factor and prefer to use a blanket "factor" on every test, on every engine or vehicle. Simple inertia dyne systems aren't capable of deriving "inertial mass" and are forced to use the same assumed inertial mass on every vehicle.

Using Steady State testing eliminates a Sweep Test rotating inertial mass error, as there is no acceleration during a Steady State test.

Transient Test Characteristics: Aggressive throttle movements, engine speed changes, and engine motoring are characteristics of most transient engine tests. The usual purpose of these tests are for vehicle emissions development and homologation. In some cases, the lower-cost eddy-current dynamometer is used to test one of the transient test cycles for early development and calibration. An eddy current dyne system offers fast load response, which allows rapid tracking of speed and load, but does not allow motoring. Since most required transient tests contain a significant amount of motoring operation, a transient test cycle with an eddy-current dyno will generate different emissions test results. Final adjustments are required to be done on a motoring-capable dyno.

### Engine dynamometer

HORIBA engine dynamometer TITAN

An engine dynamometer measures power and torque directly from the engine's crankshaft (or flywheel), when the engine is removed from the vehicle. These dynos do not account for power losses in the drivetrain, such as the gearbox, transmission or differential etc.

### Chassis dynamometer

Saab 96 on chassis dynamometer
Example: 48" Chassis Dynamometer

A chassis dynamometer measures power delivered to the surface of the "drive roller" by the drive wheels. The vehicle is often parked on the roller or rollers, which the car then turns and the output is measured.

Modern roller type chassis dyne systems use the Salvisberg roller,[2] which improved traction and repeatability over smooth or knurled drive rollers.

On a motorcycle, typical power loss at higher power levels, mostly through tire flex, is about 10% Template:Citation needed and gearbox chain and other power transferring parts are another 2% to 5% Template:Citation needed.

Other types of chassis dynamometers are available that eliminate the potential wheel slippage on old style drive rollers and attach directly to the vehicle's hubs for direct torque measurement from the axle. Hub mounted dynos include units made by Dynapack and Rototest.

Chassis dynos can be fixed or portable.

Modern chassis dynamometers can do much more than display RPM, horsepower, and torque. With modern electronics and quick reacting, low inertia dyne systems, it is now possible to tune to best power and the smoothest runs, in realtime.

In retail settings it is also common to "tune the air fuel ratio", using a wideband oxygen sensor that is graphed along with RPM.

Some, dyne systems can also add vehicle diagnostic information to the dyno graph as well. This is done by gathering data directly from the vehicle using on-board diagnostics communication.[3]

Emissions development and homologation dynamometer test systems often integrate emissions sampling, measurement, engine speed and load control, data acquisition, and safety monitoring into a complete test cell system. These test systems usually include complex emissions sampling equipment (such as constant volume samplers or raw exhaust gas sample preparation systems), and exhaust emissions analyzers. These analyzers are much more sensitive and much faster than a typical portable exhaust gas analyzer. Response times of well under one second are common and required by many transient test cycles.

Integration of the dynamometer control system along with automatic calibration tools for engine system calibration is often found in development test cell systems. In these test cell systems, the dynamometer load and engine speed are varied to many engine operating points, and selected engine management parameters are varied and the results recorded automatically. Later analysis of this data may then be used to generate engine calibration data used by the engine management software.

Because of frictional and mechanical losses in the various drivetrain components, the measured rear wheel brake horsepower is generally 15-20 percent less than the brake horsepower measured at the crankshaft or flywheel on an engine dynamometer.[4] Other sources, after researching several different "engine" dyno software packages, found that the engine dyno user can integrally add "frictional loss" channel factors of +10% to +15% to the flywheel power, raising the claim that 20% to 25% or even more power is actually lost between the crankshaft at high power outputs.

Drag racing: 1/4 mile prediction based on dynamometer measured power Horsepower figures are a strong predictor but do not guarantee a specific 0-60 mph, 1/4 mile elapsed time (ET) or 1/4 mile speed. An engine accelerating in a vehicle experiences different conditions than on a dyno. G forces and different temperatures as well as different modes of vibration in a vehicle can cause significant differences in power output.

Inexpensive "inertia dynamometers" commonly provide insufficient loading, and complete their "test" in less time than the real world 1/4 mile takes, causing inherent power value errors, due to unrealistic internal engine temperatures.

More sophisticated dyno systems are capable of "loaded testing," which can potentially recreate the same temperatures as on the drag strip.

In engineering units, the power figures used should be "True" or "Effective" horsepower scale.

Engine damage: Can dyno testing damage engines?

A brake dyno, in steady state mode only provides a load that is equal the amount of power that the engine is making at any specifically selected RPM point. If the engine makes 200 brake HP at 5000 RPM, the dynamometer's brake or power absorber will provide exactly 200 hp (150 kW) of load against it, keeping the RPM at 5000 RPM.Template:Fix

That's a realistic load that simulates a vehicle pulling a large trailer up a hill. It should be no problem on the dyno if there's no problem on the road.

Apprehension over dyno testing and engine damage has solid roots in fact. Old style dynamometers commonly used an inexpensive water brake type of power absorber. Load was increased or decreased by filling and draining water in the housing to change the amount of internal water volume to change the load, all the while draining and refilling the water to keep the water from boiling. It would sometimes take some time for the operator or computer to stabilize inflow and outflow rates. That extra time could pose a risk to engines.

Water brakes are still commonly used in applications where their small size and light weight are important and engine torque curves are relatively straight, as in large automotive and boats.

Engine testing may damage engines primarily due to insufficient instrumentation, insufficient safety monitoring systems, and insufficient cooling. An engine on a dyno does not receive air cooling due to engine speeds. Automotive engines are not typically designed for wide-open throttle operation for extended periods of time; internal components may overheat and fail.

## History

Graham-Desaguliers Dynamometer. Invented by George Graham and mentioned in the writings of John Desagulier in 1719.[5] Desaguliers modified the dynamometer and it became known as Graham-Desaguliers dynamometer.

Regnier dynamometer. Invented and made public in 1798 by Edme Régnier a French rifle maker and engineer.[6] the Régnier dynamomter.

Marriot's patent weighing Machine,[7] patent dated June 1817[8] to Siebe and Marriot of Fleet Street, London for an improved weighing machine.

Gaspard de Prony invented the de Prony brake in 1821.

Macneill's road indicator. Invented by John Macneill in late 1820s and further developing Marriot's patent weighing machine.

Froude Hofmann of Worcester, UK, manufactures engine and vehicle dynamometers. They credit William Froude with the invention of the hydraulic dynamometer in 1877 and say that the first commercial dynamometers were produced in 1881 by their predecessor company, Heenan & Froude.

In 1928, the German company "Carl Schenck Eisengießerei & Waagenfabrik" built the first vehicle dynamometers for brake tests with the basic design of the today's vehicle test stands.

The eddy current dynamometer was invented by Martin and Anthony Winther in about 1931. At that time, DC Motor/generator dynamometers had been in use for many years. A company founded by the Winthers, Dynamatic Corporation, manufactured dynamometers in Kenosha, Wisconsin until 2002. Dynamatic was part of Eaton Corporation from 1946 to 1995. In 2002, [2] Dyne Systems of Jackson, Wisconsin acquired the Dynamatic dynamometer product line. Starting in 1938, Heenan & Froude manufactured eddy current dynamometers for many years under license from Dynamatic and Eaton.[9]

## Notes

1. [1] Dynamometry
2. http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&p=1&u=%2Fnetahtml%2FPTO%2Fsearch-bool.html&r=10&f=G&l=50&co1=AND&d=PTXT&s1=salvisberg&OS=salvisberg&RS=salvisberg
3. Elisa Faustrum. "DynoJet Data-Link Module". Modular Fords. Archived from the original on September 28, 2007. Retrieved June 14, 2007.
4. John Dinkel, "Chassis Dynamometer," Road and Track Illustrated Automotive Dictionary, (Bentley Publishers, 2000) p. 46.
5. Burton, Allen W. and Daryl E. Miller, 1998, Movement Skill Assessment
6. Régnier, Edmé. Description et usage du dynamomètre, 1798.
7. Marriot's patent weighing machine
8. Marriott's improved weighing machine
9. Winther, Martin P. (1976). Eddy Currents. Cleveland, Ohio: Eaton Corporation.

## References

• Winther, J. B. (1975). Dynamometer Handbook of Basic Theory and Applications. Cleveland, Ohio: Eaton Corporation.
• Martyr, A; Plint M (2007). Engine Testing - Theory and Practice (Third ed.). Oxford, UK: Butterworth-Heinemann. ISBN 978-0-7506-8439-2. ar:دينامومتر