The Physics of

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The Physics of

• Electric Vehicles

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The Physics of

• Electric Vehicles
• By
• Russ Lemon
• Russ_at_FarTooMuch.Info

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How they work

• And why

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Electric Vehicles

• What follows is a discussion of how chemical
  energy is converted into electric energy and then
  into mechanical energy to propel a vehicle. The
  discussion includes how mechanical energy is used
  to overcome the vehicle losses of tire and
  aerodynamic drag, and yet have enough energy left
  over to climb hills and accelerate the vehicle.
• To go fast and far, minimize your losses.

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William Thomson

• aka Lord Kelvin 1824-1907
• When you can measure what you are speaking
  about, and express it in numbers, you know
  something about it but when you cannot measure
  it, when you cannot express it in numbers, your
  knowledge is of a meager and unsatisfactory kind
  it may be the beginning of knowledge, but you
  have scarcely, in your thoughts, advanced to the
  stage of science.

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Basic Units

• A decimeter is a tenth of a meter, or about 3
  15/16 inches
• A cubic decimeter is a liter
• A liter of cold water has about 1 kg of mass
• In San Diego that 1 kg of mass has a weight of
  about 9.8 newtons (force)
• Raise it up 1 meter and you have done 9.8 joules
  of work.
• Raise it up 1 meter in one second requires a
  power of 9.8 watts.

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Energy

• energy force x distance
• joules newtons x meters
• joules volts x coulombs
• 1 kW-hr 3.6 MJ megajoules
• 1 hp-hr about 2.7 MJ
• 1 BTU about 1054.8 J

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Power

• power force x speed
• watts newtons x meters/second
• watts volts x amps
• one horsepower 746 watts
• one horsepower lbf x mph / 375
• (i.e. 1 hp 5 lbf _at_ 75 mph)
• 1 hp ft-lb x rpm / 5252

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Rolling Resistance

• Rolling resistance of an average Radial Ply
  Passenger Tire inflated to 32 psi is about 1 of
  the weight on the tire.
• Rolling resistance of an average Bias Ply Tire
  can be more than double that of a radial ply tire
  with the same load and pressure.
• Rolling resistance is measured at maximum
  inflation pressure and increases as tire pressure
  decreases.

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Rolling Resistance 2

• For a vehicle weighing 4000 lb, a rolling
  resistance of 1 of load represents a drag of 40
  lb.
• At 60 mph, a drag of 40 lb represents a loss of
  6.4 horsepower or about 4.8 kW.
• There are now special low rolling resistance
  passenger tires with a rolling resistance as low
  as 0.6 of load.

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Air Resistance

• Air Resistance is proportional to the density of
  the air, the drag coefficient of the vehicle, the
  frontal area of the vehicle, and the speed of the
  vehicle squared.
• Typical Coefficient of Drag (Cd) for a modern
  passenger vehicle with windows rolled up is
  about 0.4. The EV1 was about .19. The Aptera is
  about .11

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Air Resistance 2

• For a vehicle with a frontal area of 30 ft2,
  traveling at 60 mph at sea level with a drag
  coefficient of 0.4, the drag would be about 110
  lb.
• That would be about 17.7 horsepower or about 13.2
  kW.

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Air Resistance 3

• Power needed to overcome air resistance increases
  with the cube of the vehicles velocity.
• Going from 60 to 75 mph is an air resistance
  power increase of 95
• Energy to overcome air resistance to go a fixed
  distance, increases with the square of the
  vehicles velocity. (GPM or KW-hr)

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Very High Drag
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Cd between 0.4 0.5?
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Cd about 0.19
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Cd about 0.11
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Climbing Hills

• The maximum freeway grade is 6
• Some San Diego roads have grades as high as 24.
• The force needed for a 4000 lb vehicle to climb a
  6 grade is 240 lb.
• To climb a 6 grade at 60 mph, A 4000 lb vehicle
  needs an additional 38.4 horsepower or about 29
  kW more.

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Acceleration

• If you drop something, it will accelerate at the
  rate of about 22 mph/sec. This is know as a 1 g
  acceleration.
• An horizontal acceleration of half that, or about
  10 mph/sec would be an aggressive, typical of a
  sports car with a very fast driver.
• An acceleration of 2 mph/sec would be
  conservative, typical of an older driver, or of
  a Honda Civic or VW GT.

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Acceleration 2

• An acceleration of 2.2 mph/sec, or 0.1 g, of a
  4000 lb vehicle would require a force of 400 lb.
• At 60 mph, this would require an additional 64
  horsepower or about 48 kW more.

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Losses

• Roughly 4.8 13.2 or 18.0 kW would be needed to
  maintain 60 mph on a level road with a 4000 lb
  vehicle with typical radial tires and a cross
  section of 30 ft2 with a Cd of 0.4.
• Roughly 18.0 28.6 or 46.6 kW would be needed to
  maintain 60 mph up a 6 grade.
• Roughly 47 36 or 83 kW would be needed to
  accelerate at 2.2 mph/sec up the 6 grade at 60
  mph.

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Losses 2

• Running 18 kW for 40 minutes run would be 12
  kW-hr of energy for a distance of 40 miles at 60
  mph.
• With a battery pack of 144 volts, this would be
  about 90 amp-hr of usage.
• For long life of a Lead-Acid battery, the depth
  of discharge should be less then 80. Even an
  80 DOD would shorten the life. A 100 DOD would
  give a very short life.
• Thus the need for at least a 120 amp-hr battery
  for the described vehicle.

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Measure Losses

• It takes a force equal to the weight of the
  vehicle to cause a 1 g deceleration
• A 1 g deceleration is about 22 mph/sec
• Measure how long it takes on a level road to
  coast from 65 to 55 mph in sec (t)
• Deceleration (d) (65-55)/t mph/sec
• Force (f) is vehicle weight d/22 lbs
• Loss is about f 60 /375 horsepower
• ( 1 hp 375 lb-mph 746 watts )

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Battery 1

• The source of energy for an electric vehicles is
  its battery.
• The battery must supply enough current to the
  electric motor in order for it to supply the
  needed torque.
• The battery must have enough voltage to force the
  needed current through the electric motor for the
  desired speed.
• The battery must have enough energy to supply the
  needed power for the needed amount of time.

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Battery 2

• U. S. Battery makes an 8 volt battery with a 75
  amp discharge time of 85 minutes called the
  US-8VGC.
• It has a weight of about 65 lb.
• 18 batteries in series will supply 144 volts.
• 18 batteries will weight about 1170 lb.
• Amp-Hr rating of about 106 min _at_ 75 A.
• (178 amp-hr _at_ 20 hr rate)

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Battery 3 rules of thumb

• Lead-acid batteries in an electric vehicle need
  to be at least 33 of a good vehicles gross
  weight to get a range of more than 40 miles with
  conservative driving.
• To get good performance, you need at least 33 of
  the vehicles gross weight to be active, on-line
  battery.

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Battery 4 lead-acid battery life

• Do not exceed 80 depth of discharge.
• Keep battery voltage within normal range. For
  144 V pack, keep pack above 120 V and below 185 V
  at all times.
• Limit maximum current. Excessive current leads
  to short life and even battery failure. Keep
  maximum current below the current that gives a
  full charge to 80 Discharge time of 20 minutes.
  

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Drive Train

• The electric motor must have enough torque to
  overcome the losses, climb hills and accelerate
  the vehicle to a useful speed.
• The electric motor must have enough speed for the
  vehicle.
• Gears are used to match the electric motor
  characteristics to the vehicle requirements.

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Drive Train 2

• Selected tire size is P185/60R14
• Tire will make 888 revolutions per mile
• Each tire will hold 1047 lb at 35 psi
• Total gear ratio is 3.751
• Motor RPM _at_ 60 mph is 3330
• Maximum gross vehicle weight (including 143 lb
  motor, 1134 lb of batteries, 50 lb of controller
  wiring, two 250 lb occupants and 250 lb of
  stuff) is 3700 lb.

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Electric Motor

• Series wound direct current motor
• In any gear, speed is proportional to RPM
• Constant torque for even acceleration
• Torque roughly proportional to current
• Increasing voltage is necessary to maintain
  current to maintain torque as vehicle speed and
  motor RPM increase
• Batteries must have enough voltage and current to
  maintain desired speed

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Electric Motor 2

• The selected electric motor is the Advanced DC
  FB1-4001
• Diameter is 9.1
• Weight is 143 lb
• Max continuous rated current is 180 A
• Max 1 hour rated current is 200 A
• Max 5 minute rated current is 340 A
• Current is limited by motor temperature
• Motor speed should be kept under 6000 rpm High
  rpm causes rapid brush and bearing wear.

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Motor Characteristics

• Torque increases with current.
• Back voltage increases with current and motor
  speed rpm.
• Motors are also a generator.

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Vehicle Characteristics

• You select with your foot the current sent to
  the electric motor. With a constant current you
  have a constant torque. As the vehicle
  accelerates from a stop, the controller increases
  the voltage on the motor to maintain that current
  until there is no more voltage. battery voltage
  reached As the vehicle continues to accelerate,
  current and therefore torque decrease, causing
  acceleration to also decrease until torque is
  just enough to match losses and you maintain a
  constant speed.

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Vehicle Characteristics 2

• In the following graph, for a given foot
  setting, you follow a constant torque line up to
  the battery voltage and then follow a horizontal
  line to the right as rpm and vehicle speed
  increase. Note the corresponding decrease in
  torque.
• You must have enough battery voltage to push
  the current you need to get the torque you need
  to go the speed you need.

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Assumptions

• Battery voltage is 144 volts.
• Maximum controller current is 500 amps.
• Motor is Advanced DC FB1.
• Vehicle gross weight is 4000 lb.
• Tire drag is 1 of vehicle weight.
• Aerodynamic Cd is 0.4.
• Cross sectional area is 30 ft2.
• Vehicle is at Sea Level.

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Warning

• Note that the highest force in the previous
  slide is for a current of almost 500 A that will
  quickly overheat the motor. The continuous
  current must be less then 180 A and that means
  that the continuous force must be less than 1/3
  of the maximum force shown.

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Motor Comment

• Remember that power is the product of torque
  and rpm. With the ADC FB1-4001, the 200 A
  continuous rating is a torque limit of about 30
  ft-lbs. At 30 ft-lbs, it takes about 144 V for a
  motor speed of 5500 rpm. This is about 31 hp.
  Actually, I2R losses in battery, controller and
  wiring will reduce the actual voltage available
  to the motor. At 80 DOD with a 200 A load, the
  maximum voltage at the motor may be as low as 120
  V for only 4500 rpm. 25 hp

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Motor Comment 2

• Gearing the motor for 4500 rpm at the top
  vehicle speed 70 mph? will take full advantage
  of the capability of the battery, controller and
  motor in the real world.
• Too many car conversions fail to take into
  account worst case conditions. The last hill to
  climb with batteries at 80 DOD. Of course some
  have the option to shift to a lower gear and
  struggle at a lower speed.

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Measure Performance

• It takes a force equal to the weight of the
  vehicle in addition to the force to over-come
  losses to cause a 1 g acceleration.
• Measure how long it takes on a level road to
  accelerate from 55 to 65 mph in seconds (t).
• Acceleration (a) at 60 mph is about 10/t.
• Force (f) is about weight a/22 lbs.
• Acceleration Hp is about f 60 / 375.
• Total Hp is Acceleration Hp Loss Hp.

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Range

• Now that we have a rough idea of the vehicles
  performance, the next question is how far will it
  go on a charge. In other words, what is its
  range? Range should really be determined by how
  far it will go on 80 of a charge since
  completely discharging a battery will ruin it.
  Note that the capacity amp-hr decreases as the
  current increases. Also note that the voltage
  decreases as the charge is used up.

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Range 2

• To estimate range at a given speed, determine the
  force needed at that speed. The force (lb) x
  speed (mph) / 375 is the hp needed to maintain
  that speed. Multiply hp by .746 to get kW.
  Divide kW by the battery voltage to get battery
  current. Estimate battery amp-hr at that current
  and divide by the current. Multiply hr by 0.8 to
  get the approximate number of hours. Multiply
  hours by the speed to get an estimate of range.

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Available Current

• The total capacity of the battery is non-linear.
  The minutes the battery can provide power
  decreases faster then the amps supplied by the US
  8V GC battery
• 1041 minutes _at_ 10 amps
• 341 minutes _at_ 25 amps
• 146 minutes _at_ 50 amps
• 94 minutes _at_ 75 amps
• 66 minutes _at_ 100 amps
• 50 minutes _at_ 125 amps

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NOTICE

• The numbers used on the previous slides were
  taken from the best information and estimates
  available. Exact measured numbers were not
  available. Therefore, notice is given that the
  conclusions are approximate ballpark estimates.
  Actual performance to be determined.

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Charging

• U.S. Battery recommends that
• Voltage not exceed 2.585 V per cell
• Current not exceed AH/10
• Time not exceed 10 hours
• http//www.usbattery.com/pages/usbspecs.htm
• In other words, for a 144 volt pack, the
  charging current should not exceed 165/10 or
  about 16.5 amps until limited by the total
  voltage that must not exceed 186 volts. Maximum
  charge time is 10 hours. Check water level after
  charge.

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Charging

• 186 volts times 16.5 amps is 3065 watts. That
  would be about 26 amps from a 120 volt source, or
  13 amps from a 240 volts source, not taking into
  account efficiency of the charger. If time were
  short, the batteries could be charged at 25 amps.
  That would be 4650 watts, or almost 20 amps from
  a 240 volt source. A 30 amp 240 volt service is
  best for charging.

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. . . ie Hybrid

• For long trips a small motor-generator can be
  added to extend range. Motor generators are made
  to run on a variety of different fuels.
  Commercial motor-generators include gasoline,
  diesel, propane, etc. Be sure the controller can
  take the higher voltage. Voltage should not
  exceed the maximum battery charging voltage.

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• San Diego
• Car Conversion Project
• July-August 2008
• Physics of Electric Vehicles
• by
• Russ Lemon
• Russ_at_FarTooMuch.Info

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The End

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To Return

• http//EVAoSD.com