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Ball Park Approximations

Major Forces on a Vehicle

Note:
speed in MPH, weight in lb. mass, area in ft^2, torque in ft-lb., time in seconds, force in lbf. tirecoef for an EV tire is about .007. (most radial tires about twice that,) air density at sea level and 20F is about .00327. dragcoef for EV1 is about 0.2. (Most cars about twice that.)

For Example:

A vehicle with a cross section area of 30 square feet (6' x 5'), a dragcoef of 0.4 at STP and a velocity of 60 mph will develop a force of:

F = .00327 * 0.4 * 30 * 60 * 60 = 141 lb. and

require 22.6 horsepower to overcome wind resistance.


For Example:

A vehicle with a weight of 4000 lb with regular radial tires with a tirecoef of 0.01 will develop a force of:

F = 4000 * 0.01 = 40 lb. and, at 60 mph,

require 6.4 horsepower to overcome rolling resistance.


For Example:

A vehicle with a weight of 4000 lb going up a 5% grade will develop a force of:

F = 4000 * 0.05 = 200 lb. and, at 60 mph,

require 32 additional horsepower to overcome the grade.


For Example:

To accellerate a 4000 lb vehicle from 54 to 65 mph in 5 seconds will require an additional force of:

F = 4000 * ((65-54)/5) / 22 = 400 lb. and

require 64 additional horsepower to accellerate.
(average speed is (65+54)/2 mph.)

Steady Force=tirecoef x weight + air density x dragcoef x area x speed2
(at sea level and normal temperature)

Acceleration Force = (weight/22)*(speed2-speed1)/(time2-time1)

Hill Force = weight * sin(grade)

Total Force = Steady Force + Acceleration Force + Hill Force

Horsepower = Total Force * speed / 375 = torque * RPM / 5252

"A pints a pound the world around." Old English measure of water.
A Cubic Meter of Water has a mass of a metric ton [megagram].
For the same volume,
Aluminium weighs about 2.7 times as muchas water,
Iron weighs about 7.9 times as much as water,
Lead weiths about 11.4 times as much as water, and
Gold weighs about 19.3 times as much as water.

A British Thermal Unit (BTU) is 0.293 watt-hr or 1054.8 joules.
An SDG&E Therm is 100,000 BTUs or 29.3 kW-hr.


Advanced DC Motors Model 203-06-4001

amps = (5 * torque) + 85 . [rough approximation]

RPM = (286 * volts) / (10 + torque)0.5 . [rough approximation]

The Advanced DC Motor Model 203-06-4001 is a typical, series wound motor that is often used in Electric Vehicles. It can be reasonably characterized with the above two equations. It is 8 inches in diameter, almost 15 inches long (not including shaft), and weighs about 107 pounds. It is designed for a maximum voltage of 120 volts. With an input of 91 volts and 178 amps, it can continuously deliver 19 horsepower at 5000 rpm. With an input of 86 volts and 322 amps, it can deliver 31.5 horsepower at 3600 rpm for 5 minutes. Both of these ratings assume standard ambient temperature. Maximum speed is about 8000 rpm, but results in greatly increased brush wear.

It should be noted, that comparing electric motor with gasoline engines is like comparing apples and oranges. Gasoline engines are rated at their peak power, and electric motors are rated at their continuous power. It is for this reason that a 30 hp electric motor will generally perform like a 50 hp gasoline engine in a same weight vehicle. Of course the addition of a large number of batteries will diminish the vehicle's ability to accelerate or climb hills.


Metric Approximations

With the move to international trade is the move to Metric Units. Metric Units are, of course, based on powers of ten, and the physical characteristics of water. The internaltional unit of length is the meter. By definition, there are exactly 39.37 inches in a meter. A cubic meter of water has a mass of one million grams, also known as a megagram or metric ton. Acceleration of gravity on Earth is about 9.8 meters per second squared. The unit of force is the Newton. The unit of power is the Watt which has the units of Newton-Meter. And the unit of energy is the Joule which is a watt second. From this we calculate the following:

To raise one metric ton 100 meters is a megawatt-second, which is also 0.277 KiloWatt-Hour or 0.372 Horsepower-Hour. If a heavy object is dropped from 100 meters, it will crash into the Earth at 44.27 meters per second, or about 160 KiloMeters per Hour or about 100 miles per hour.

One KiloWatt-Hour is 3600000 watt-seconds. On Earth it is enough energy to raise a metric ton 367 meters. If a heavy object is dropped from 367 meters, it will crash (into the Earth) at 84.85 Meters per Second, which is equivalent to 305.47 Kilometers/Hour or about 190 miles/hour. i.e. a KW-hr will accerate a metric ton to 305 KM/Hr or 4 metric tons to 153 Km/Hr (about 85 mph).

Similiarly, it would take 60 Kilowatts (about 80 hp) to raise a metric ton (about 2204 lb) 367 meters (about 1204 feet) every minute. At 100 KM/hr (62.137 mph), that would be a grade of about 22% (367*60*100/100000).



Metric Prefixes

With English unit, we add a sufix to denote very large or very small quantities. For example, "seven million" In metrix a prefex is added to the unit, as in "seven megabucks" which would be seven million dollars. Similarly a kilobuck would be $1000, a decibuck would be a dime and a centibuck would be one cent. Below is a list of some of the prefexes used by the metric system preceded by their abreviation.

 
          (T)  tera    1000000000000
          (G)  giga    1000000000
          (M)  mega    1000000
          (k)  kilo    1000
          (h)  hecto   100
          (dk) deca    10
          (d)  deci    0.1
          (c)  centi   0.01
          (m)  milli   0.001
          ()  micro   0.000001
          (n)  nano    0.000000001
          (p)  pico    0.000000000001
 

Note that "" is the greek letter mu. Only in the United States medicine has the 'g' (microgram) been replaced by 'mcg'.

Please DO NOT confuse "m" and "M". Asprin is measured in mg (milligrams) and cars are measured in Mg (megagrams) which are known as 'metric tones'. A mm is the small mark on a ruler showing tenths of a centimeter but a Mm is approximetly the distance between Salt Lake City and San Diego.

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