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July 2004
The following units and formulas are used in calculating the power and energy needs of vehicles based on the requirements of speed and acceleration.
Fundamental Units
Fundamental units are those measurements which cannot be derived must must be measured.
All other formulas can be derived from the fundemental units.
The fundamental units that are used for motion are:
| Quantity |
Units |
Symbol |
length/distance
|
metres (m) |
d |
mass
|
kilogram (kg) |
M |
time
|
second (s) |
T |
temperature
|
degrees Kelvin (oK) |
(theta) |
Velocity/Speed
Speed is the measurement of the movement of an object. Velocity is the speed plus direction.
| Units |
Symbol |
Formula |
meters per second (m/s)
|
v |
v = d t |
Acceleration
Acceleration is the rate of change of speed. A negetive acceleration is commonly called deceleration.
| Units |
Symbol |
Formula |
meters per second squared (m/s2)
|
a |
a = (v1 - v0) / t
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Distance
Distance travelled based on a speed/acceleration
| Units |
Symbol |
Formula |
meters (m)
|
d |
d = v0 t + 1/2 a t2 |
Force
Something trying to move a mass.
| Units |
Definition |
Symbol |
Formula |
Newtons (N)
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1 Newton of force is produced by acceleration of 1 kg of mass 1 m/s2
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F |
force = mass * acceleration
F = m a
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Weight
Weight, is not the same as mass. Weight is a measurement of the force of gravity on a mass. A mass for a given object is always the same no matter the force of gravity (e.g. the moon)
| Units |
Symbol |
Formula |
Newtons (N)
|
w |
weight = mass * acceleration of gravity (9.8m/s2)
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Pressure
Force per unit area
Click here for info on tensile strength.
| Units |
Definition |
Symbol |
Formula |
Pascal (Pa)
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1 Pascal of pressure = 1 Newton of force applied over 1 square metre
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?? |
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Work
A force moving a mass a distance.
| Units |
Definition |
Symbol |
Formula |
Joules (J)
kg m2/s2
Newton-meters (N m)
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1 Joule of work is produced by applying 1 Newton of force to move an object 1 metre
|
W |
work = force * distance
W = F d
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Energy
The ability (or capacity) to do work
| Units |
Definition |
Symbol |
Formula |
Joules (J)
Watt-hours
Calories
BTU
|
|
E |
Ek = 1/2 m v2
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Power
The rate at which energy is used.
The rate at which work is done.
| Units |
Definition |
Symbol |
Formula |
Watts (W)
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1 Watt = 1 Joule per second
1 Watt = 1 Volt times 1 Ampere
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P |
P = V * I
P = W / t
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Torque
A force that rotates an object around a point.
A torque is not the same as work, although it is measure in the same units.
The distance portion of the torque is the distance from the centre of rotation to the point of the force,
unlike work, the distance is how far the force moves an object. To determine the amount of work a torque applies
to its' point of rotation, you must multiple the torque by the distance the object is rotated through its' centre.
| Units |
Definition |
Symbol |
Formula |
Newton-meters (Nm)
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1 Nm force is create by applying a force to a lever of 1 Newton, 1 metre from the point of rotation
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T |
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Rotational Work
The amount of work perfomed by a torque force rotating an object
| Units |
Definition |
Symbol |
Formula |
Newton-meters (Nm)
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Power - Torque Relationship
Power and torque do have a relationship:
Power = work / time
Power = torque * RPM * (1min/60sec) * 2 * pi
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Power is generally low at low RPMs because the rate at which the force (rotational work) is applied is low.
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