Power and Its Measurement

1
Power and Its Measurement
Roy S. Walls, Jr. Institute of Applied Agriculture
2
Objectives

• Define terminology related to power and its
  measurement, i. e. energy, force, work, torque,
  horsepower, watt
• Interpret information on power ratings of
  agricultural power units to select appropriate
  power units.
• Measure horsepower with a dynamometer and plot
  horsepower / torque curves
• Interpret dynamometer test results and make
  recommendations for improving power performance.

3
Terms and definitions

• Energy - capacity or ability to do work, can not
  be created or destroyed, only changes from one
  form to another
• Potential energy
• Position- water stored behind a dam
• Chemical - motor fuels
• Condition - a spring compressed
• Kinetic energy - energy in motion,
• Water falling over a dam
• Rotating power shafts
• A spring released

4
Energy

• Example A heavy weight suspended on a rope
  contains energy potential. When the rope is cut,
  potential energy turns into kinetic energy as the
  weight falls.
• When the weight hits the ground, the kinetic
  energy is dissipated in three ways sound, heat
  (absorbed by the soil, and compaction of the
  earth
• Engines convert a fuels potential energy into
  useable kinetic energy. The process generates
  tremendous heat. Two thirds of this heat is lost
  to exhaust and engine cooling and only 1/3 of
  the heat generated is used to power machinery
  components.

5
Force

• action that attempts to move of an object from a
  state of rest or causes a change of speed or
  direction of an object in motion
• expressed in terms of weight, e.g. pounds, tons,
  kilograms

6
Work

• results when force (pounds, tons, kilograms)
  overcomes a resistance and causes movement of an
  object over a distance (feet, yards, meters).
• The formula to calculate work isWork
  Distance X Force

7
Work Calculation

• If an object that weighs 330 pounds is moved a
  distance of 100 feet then 33,000 foot pounds of
  work has been completed
• 100 ft X 330 lbs 33,000 foot pounds of work
• Note if no movement results upon the application
  of force, no work is accomplished.
• Motion must occur for work to be calculated.

8
Types of Work

• Linear motion is usually expressed as foot
  pounds of work.
• Rotary motion (torque) is usually expressed at
  pound feet.
• Mathematically, the units are the same.

9
Power

• Power is the rate (time interval) at which work
  is accomplished.
• Expressed as foot pounds per minute or second
• pound feet per minute (torque)
• POWER work time

10
Sample Calculation

• object weighing 330 pounds was moved 100 feet, in
  one minute, then work at the result of 33,000
  foot pounds / minute was accomplished.
• This is equal to one horsepower.
• Power Force X Distance or Work (ft
  lb) Time Time
• 330 lbs X 100 ft 33,000 ft lbs
• 1 min min

11

• If a 330 lb. weight 100 ft. in 1/2 minute
• 330 lbs X 100 feet 66,000 ft lbs
• .5 min min
• The amount of work (foot pounds) in this example
  is the same but the rate or time interval is
  different. Twice as much power was exerted in
  the second example because the same amount of
  work was completed in half the time as the first
  example.

12
Horsepower

• Standard unit of engine power associated with an
  amount of work accomplished over specified time
  intervals and can be expressed in several ways.
• Horsepower was originally defined by James Watt
  in 1765 when trying to compare steam engines with
  the known power source of that era (the draft
  horse).

13
Watt Takes Notes at the Dock

• James Watt (1780s) observed that a draft horse
  could move a 330 pound weight a distance of 100
  feet in a time of one minute.
• This is equal to 33,000 foot pounds per minute or
  one horsepower
• This fact has been used as our standard for
  horsepower measurements ever since.

14
Horsepower
100 Feet in 1 minute
330 Lbs
15
Horsepower Formulas

• There are many formulas for computing horsepower
  (Hp) but they are derived from the following
  expression that
• One Hp 33,000 ft lbs of work per minute
• several other mathematical formula have been
  derived from this basic formula to calculate
  horsepower

16
Formulas

• Hp Force (lbs) X Distance (feet)
• Time (minutes) X 33000 ft. lbs/min
• Problem A tractor pulls a wagon weighing three
  tons and exerts a force of 3,000 pounds. If the
  load is moved 400 feet in one minute, what is the
  horsepower developed? What if it took two
  minutes to pull the same load this distance?

17
Solution

• 3,000 lb x 400 ft 1,200,000
  36.36 Hp33,000 ft lb/min. X 1 min 33,000
• 3,000 lb x 400 ft 1,200,000
  18.18 Hp33,000 ft lb/min. X 2 min 66,000
  

18
Time given in seconds

• 33,000 ft lb 33,000 ft lb 550 foot
  pounds
• 1 min 60 sec 1 sec
• Hp Force (lbs) X Distance (feet)
• second(s) X 550 ft lbs/sec
• One Hp 550 foot pounds per second
• 33,000lb ft/ min / 60 sec 550 ft lb per sec.

19

• Example Calculate horsepower considering 500 lb
  load was moved 100 feet in two seconds.
• 500 lb X 100 ft 50,000 45.45
  Hp
• 550 ft lb/sec X 2 sec 1100

20
Drawbar horsepower formula

• the drawbar horsepower formula is useful when
  distance is given in miles per hour (mph).
• Hp draft( pounds of force) X mph
• 375

21
Sample

• Example A tractor pulling a mower generates a
  draft (force) of 1800 pounds on the drawbar. If
  the tractor is traveling at 5 miles per hour,
  what is the horsepower exerted.
• We can work this problem in with a couple methods.

22
How do we do this?

• Hint convert MPH to ft./min. or ft./sec. or use
  the drawbar Hp formula.
• To convert mph to feet per minute
• 5 mile X 5280 ft X1 hr 440 feet
• 1 hr x 1 mile x 60 min min
• 5 mph 440 ft per minute, now use original Hp
  formula

23

• Force (lbs) X Distance (feet) Hp
• Time (min) X 33000 ft lb/min
• 440 ft X 1800 lb 792,000 24 Hp
• 1 min X 33000 ft lb/min 33,000

24
Use drawbar formula

• draft(force) X mph Hp 375
• 1800 X 5 9000 24 Hp
• 375 375

25
Torque

• force which attempts to produce rotation of an
  object (shaft, gear, pulley, etc.).
• If motion occurs, we can calculate work which
  is accomplished through rotational energy, such
  as by pulleys, crank arms, gears, belts, chains,
  etc.

26

• Example A winch could be used to drag or lift a
  330 lb. load 100 ft and the same amount of work
  is the result - 33,000 pound feet

27
Winch Working

• If a winch lifts 330 pounds a distance of 100
  feet in one minute then 33000 lb. ft of work or
  one horsepower was developed.
• 330 lbs. X 100 feet 1 Hp
• 1 min x 33,000 ft lb/min

28

• In machinery, torque is typically measured in
  terms of force (lbs) and distance (ft).
• Force is the pounds of force (weight) applied to
  the lever arm.
• Distance involved is the length in feet of the
  lever arm involved (radius of a pulley, gear or
  sprocket).

29
Torque pound feet

• Torque is expressed as pound feet rather than
  foot pounds.
• Mathematically the work produced is the same.

30
Linear vs Rotational Work

• With linear work feet is the distance an object
  is moved and force is the weight of the object
  being moved. Foot times pounds of force foot
  pounds
• With torque feet is the distance of the lever
  arm (radius of pulley, gear, etc,) involved and
  force is the pounds of effort being applied to
  the lever arm

31
Torque formula

• Example An engine delivers 400 pound feet of
  torque at 1000 RPM. Calculate the horsepower
  using the torque formula.

32
Torque Formula

• HP Torque (lb ft) X RPM
• 5252
• 400 lb ft X 1000 RPM 400,000 76.16 HP
• 5252 5252

33
Derivation of horsepower formula for testing
rotating power sources

• Hp Torque (pound feet) X RPM (speed of rotating
  shaft)
• 5252
• 1. Hp Force (pounds) X Distance (feet)
• Time (minutes) X 33000
• Note omit time because RPM is in revolutions per
  minute
• 2. Distance of rotating lever arm RPM X 2 p
  Length of lever arm or
• 3. D RPM X 2 X 3.1416 X L (substitute this in
  line 1)
• 4. D Force (pounds) X RPM X 2 X 3.1416 X L
• 33000
• 5. Hp F X RPM X L
• 5200
• 6. Torque (T) F X L (substitute 6 in 5)
• 7 Hp Torque X RPM
• 5252

34
Electric motor horsepower has a wattage equivalent

• Wattage equivalent for electrical energy
• Watts Volts X Amps
• One Hp 746 watts of electrical energy _at_ 100
  efficiency.
• A typical 1 Hp electric motor 1000 watts
• A 240 volt motor drawing 10 amps consumes 2400
  watts or 2.4 hp

35
Engine Output

• Horsepower expressions (how hp is expressed) -
  several different ways of expressing horsepower
  from various engine manufacturers

36
Indicated horsepower

• power derived by engineering measurement based on
  fuel type, piston stroke, piston area, energy in
  fuel, etc.
• process subtracts the frictional engine losses
  and deals with raw power of the fuel and engine
  components. (This method is not typically useful
  to us, the consumer.)

37
Friction horsepower or Maximum power

• Power measured at the engine flywheel without any
  power consuming accessories.
• The fan, water pump, air cleaner, starter,
  alternator, exhaust system and accessories are
  removed.
• These functions are then provided externally in
  power testing labs.
• This method is generally not useful to the
  consumer, but be aware that some agricultural
  power units are rated this way.
• This rating method may be a true indication of an
  engine's power output, but is not practical for
  agricultural use.

38

• This may also be referred to as advertised,
  advertised maximum, brake, delivered, flywheel,
  gross, gross brake, maximum, maximum brake,
  maximum engine, peak, published gross engine,
  rated brake shaft, or stripped.

39
Net power

• Measured the same way as maximum power at the
  flywheel, but with normal engine accessories
  attached.
• certified, effective, guaranteed, net engine, net
  brake, rated, etc.
• This method may be practical for some
  applications (engine driven pump for example)

40
Transmitted or Observed Horsepower

• Used to measure power used at the consumer end,
  such as the rear wheels, power takeoff (PTO),
  belt, pulley, or drawbar.
• No factor corrections are made
• Best for us as power consumers use because these
  measurement methods take into consideration power
  losses from frictional sources and other
  parasitic loads such as engine accessories and
  power train losses.

41
Corrected power

• observed power corrected for atmospheric
  temperature, barometric pressure, and altitude
  conditions.
• Standard test conditions are 500 ft. above sea
  level, barometric pressure of 29.38" mercury, 85
  degrees F. ambient air temperature, with a water
  vapor pressure (relative humidity) of 0.38 " of
  water.
• Power output typically decreases 3.5 per 1000
  ft. of elevation above 1000 feet, and 1 per 18
  degrees above 60 degrees Fahrenheit.

42
Drawbar horsepower (DBHP)

• A measure of the pulling power an engine can
  produce when mounted in a moving machine.
• A load is attached and can be horsepower is
  calculated based on weight, distance and time
  factors.
• Losses of available DBHP dependent upon power
  train losses, type of tires, amount of tread
  wear, amount of wheel slippage, ballast (weight),
  soil conditions, etc.

43
PTO horsepower

• Power available to the Power Take Off (PTO) shaft
  of the tractor
• measured as a function of torque (pound feet) and
  speed (RPM) into an absorption dynamometer

44
Rated horsepower

• manufacturer's rating for expected engine power
  under normal operating conditions at a certain
  engine or PTO speed.
• Manufacturer determines maximum stresses and
  RPM's the engine can operate under without
  internal engine damage occurring.

45
Volumetric efficiency

• Ratio of available air to the engine, to the
  actual volume taken into the engine during
  operation.
• Engine generates its maximum horsepower at the
  point where it most efficiently intakes air and
  expels or exhausts the spent fuel charge.
• As engine speed increases, there is physically
  less time for air to fill the cylinder in the
  engine.
• Efforts to super charge or turbo charge an engine
  are designed to force more air into the engine
  cylinder.

46

• Atmospheric pressure is generally force to push
  air into an engine. This pressure is 14.7 psi at
  sea level and decreases with elevation.

47
Horsepower, Torque curve

• Developed from dynamometer test results by
  plotting PTO or engine speed, horsepower and
  torque developed

48
Torque curve

• Rotating effort measured on dynamometer, used to
  evaluate and diagnose engine performance
• High flat curve is ideal for agricultural use
• Power unit has good lugging ability

49
Torque reserve

• "lugging ability" of the tractor when a large
  load is applied.
• Agricultural power units are typically designed
  to provide very good lugging ability.
• Car engines typically have poor lugging ability

50
Horsepower, speed, torque relationship

• Note horsepower curve shown
• Engine horsepower (Hp) labeled on left vertical
  axis
• Engine RPM labeled on horizontal axis
• Greater horsepower is generated at higher RPM's
• Hp increases until max Hp is reached and then
  decreases as engine speed decreases
• Agricultural engines are typically rated between
  1700 - 2100 RPM

51
(No Transcript)
52

• PTO ratings typically rated at 540, 1000 RPM or
  other RPM specified by manufacturer
• Engine typically runs faster than the speed at
  which it reaches its maximum or rated Hp
• Hp decreases as engine load continues to build
  due to the increased frictional loss in the
  engine
• Engine develops less Hp as load increases due to
  loss of engine volumetric efficiency (engine
  fails to move adequate air/fuel on intake and
  fails to intake air and exhaust spent air/fuel
  efficiently)

53

• Torque Curve - note chart
• torque is typically labeled on right vertical
  axis so that Hp and torque can be compared as
  engine load increases
• measured torque shows how the engine perform in
  regards to its turning effort as engine load
  changes
• as engine load increases and engine RPM
  decreases, note that torque output increases,
  even though developed Hp output decreases

54

• torque will eventually reach a peak, additional
  load causes a continued loss of RPM, loss of Hp
  and loss of torque ("engine bogs down" or
  eventually stalls)
• manufacturer's uses peak torque as an engine
  rating (peak torque or max. torque) This may be
  useful to know when matching power units to
  implements that require power.

55

• manufacturer's usually rate ag engines at
  800-1000 RPM higher than the speed at which peak
  torque is reached to allow for torque reserve
• this allows for a "torque reserve or constant
  power" available to the operator. Operator is
  typically not aware of how the engine performs at
  this level but this factor is definitely
  measurable on a dynamometer
• engine loads can fluctuate in this torque reserve
  area and the engine compensates automatically to
  the load by increasing torque as needed

56
Torque rise

• Torque rise percentage difference in torque
  produced at engine at its rated speed and peak
  torque divided by rated torque.
• torque reserve relates to torque rise and is an
  indicator of lugging ability

57
Torque rise

• Maximum Torque Torque at rated speed X 100
• Torque at rated speed

58

• Example Tractor at its rated PTO speed produces
  400 pound feet and generated 500 pound feet peak
  or maximum torque.
• Calculate the torque rise as follows

59
Torque rise

• Maximum Torque Torque at rated speed X 100
• Torque at rated speed
• (500 lb ft - 400 lb ft) x 100 25 torque rise
• 400 lb ft

60
Testing Horsepower

• Horsepower is tested on a machine called a
  dynamometer.
• This machine applies a braking load to the
  tractor drawbar, PTO shaft, or engine flywheel.
• The braking force is applied by prony brake
• uses a brake drum (hydraulically actuated) as a
  loading device.
• The brake is attached to a lever arm (1 foot long
  typical) which transmits the turning effort
  (force) to a scale or electronic load cell.

61

• water brake dynamometer - a pump is turned and
  the water output of the pump is restricted
  causing the pump to turn harder. A lever arm
  attached to the arm transmits torque to a scale
  or electronic load cell

62
Prony brake dynamometer
63

• electric dynamometer - engine turns a generator
  and the wattage produces is an indicator of
  horsepower
• Eddy current dynamometer - engine turns a
  generator which is attached to a lever arm. As
  the generated load increases through a large
  resistor bank to dissipate the wattage produced,
  a lever arm attached to the generator applies
  torque to a scale or electronic load cell

64
Dynamometer Performance variables

• Dynamometer accuracy, operator skill
• Engine test conditions
• Fuel temperature - 18F --gt 3-4 change in HP
  output. Hot fuel is less dense, and has less
  energy and develops less horsepower
• Air temperature - 18F --gt 1 change in HP output
  in a naturally aspirated engine, no difference in
  a turbocharged engine

65

• Altitude
• air is less dense at higher elevations, and the
  same engine would develop less horsepower
• Type of fuel
• Diesel - Cetane rating
• Gasoline - octane rating
• Age of the fuel (gasoline deteriorates after
  about 30 days)
• Summer/winter fuel - formulations are different

66

• Parasitic loads from power train, differential,
  condition of lubricants
• Engine condition or wear - "well tuned", speeds
  correct (governor), clutches not slipping

67
Nebraska Test

• there is not really an official legal test for
  horsepower in USA
• 1919 - Nebraska established own state test
• has essentially become adopted as the standard in
  US
• published data readily available for tractors

68
Nebraska test includes

• PTO Hp - measured at PTO shaft
• good measure of Hp, useable Hp to the owner/user
• rated at 540, 1000 or other manufacturer.
  specified RPM
• manufacturers rate engines at their best
  performance, as it is impractical to design
  engines to perform specifically at 540 or 1000
  PTO RPM

69

• Drawbar Hp - typically measures about 10 less
  than PTO Hp
• draft (pounds of force) exerted by tractor at
  drawbar in various gears
• slippage of wheels, soil moisture, ballasting of
  tractor are definite factors
• useful in sizing a tractor to equipment with
  certain power input requirements (You cant
  sensibly pull a plow requiring 200 Hp with a 100
  Hp tractor!)

70

• Fuel use data also provided by Nebraska test
• note fuel consumption data provided
• good info to compare what sales person tells you
  versus test results
• good data to estimate projected fuel usage costs

71
Power and Its Measurement