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Basics
Engine power is a rating of how quickly work can be done. Work is a measure
of force times distance. If you lift a 550 pound object 1 foot you have
done 550 foot pounds of work (not to be confused with foot pounds of torque
which is a force, not work). This ignores inertia affects that would be
very large in this example. If you do that work in one second, you have
just applied one horsepower (or 746 Watts). The relationship between engine
torque and horsepower is:
1HP = ((torque in foot pounds)x(RPM))/5252
Torque is a force rating. A foot pound of torque is 1 pound of force
applied perpendicular to a shaft 1 foot from the shaft centerline. Torque
can be applied with no motion. A torque rating alone tells you some things
about an engine however it does not tell you how much work the engine
can do in a given time.
Power (HP or kW) is a rating of the amount of work that can be done in
a given time. Power is really the rating you need to determine how fast
you can go, how quick you can accelerate, or any other performance aspect
of a vehicle, boat, or any powered machine.
Power is conserved in a geartrain except for some loss due to friction.
Torque however, is multiplied or divided in a gear train. If you have
a 4:1 gear ratio, you will multiply your torque by 4. Applying 200 foot
pounds of torque will result in 800 foot pounds on the output. However,
if you apply 200 HP to the input, you sill get 200 HP (minus some friction
losses) out but your output shaft RPM is ¼ what it was on the input.
Engines with high torque ratings and low power ratings are engines that
build power down low, but it quickly drops off at high RPM. These engines
usually have a wide, constant power band. They are good for towing where
you need to apply power all the way through each gear for long periods.
Engines with high power and low torque are higher RPM engines. These
engines do better with more transmission speeds and higher final drive
ratios. Their power band is usually not flat but rather slopes upward
to a peak and then drops off. If you run these engines much below the
peak power RPM, the power is much lower than the peak power. If you can
keep the same peak torque rating, but double the RPM at which the peak
torque is delivered, you will double power.
Vehicle Dynamics
Newtons law states that force equals mass times acceleration (F=ma).
This equation can be solved for acceleration to show that acceleration
equals mass divided by force (a=F/m). Acceleration is the rate of speed
change and is expressed in units of length per time squared (typically
feet per second squared). Neglecting things like traction, doubling force
will double acceleration. Power is required to apply the force at a rate
fast enough to do the work of accelerating the vehicle. Doubling acceleration
will reduce the time it takes to achieve a given speed by half. Cutting
mass in half has the same affect as doubling power. Bottom line: if you
want better acceleration, reducing the mass (weight) or a vehicle will
have the same affect as increasing power (force).
Weight is simply mass times the acceleration equivalent of gravity (32.2
feet per second squared). If you divide a vehicle weight in pounds by
32.2, you will get the mass in units of slugs. If you divide the weight
in Newtons by 9.81, you get the mass in Kilograms (kg).
In high powered vehicles, traction is generally the limiting factor for
acceleration. Traction is the force the tires can apply to the pavement.
The reaction is an equal and opposite force applied to the vehicle thereby
accelerating it. It is governed by friction. There are 2 measures of friction:
kinetic (relative motion between surfaces) and static (no relative motion).
If your tires are slipping on the pavement you are using kinetic friction.
If the tires are not slipping, you have static friction. A car driving
down the road at a constant speed is using static friction between the
road and tires. Static friction is greater than kinetic. In other words,
once you slip the tires, you loose traction force, and thus loose acceleration.
Traction equals the weight applied (normal force) to the tire times the
friction coefficient. The static friction coefficient is greater than
the kinetic friction coefficient. Increasing the weight on a tire will
increase the traction, as will increasing the coefficient of friction.
Tires will have less traction when slipping.
For off-road vehicles, there is another factor to consider and that is
inertia. In soft terrain, such as soft sand, there is very little friction
available. As the tire rolls, the sand just shifts under it. In order
to propel a vehicle through this medium, you can displace enough sand
to force the vehicle forward. This is more like a boat. A boat is propelled
forward by pushing water backwards. The off-road vehicle just propels
the sand instead of water. This is why paddle type tires are used in very
soft terrain.
Gravity has the same affect on a mass as acceleration. When the car is
at rest, only the acceleration affect due to gravity is acting on the
car to produce weight (force). When the car accelerates, a second force
is required to cause the acceleration. These 2 forces are called vectors
(each having a direction and a magnitude). Linear algebra is used to combine
the vectors into a single resultant vector. This affect is generally referred
to as weight shift. What this really means is that the resultant direction
of the vector sum of the 2 force vectors is not longer perpendicular to
the earth center (gravity only).
The car will have a center of mass located at a point called the mass
centroid. This point is different than the geometric center but will typically
be somewhat near the geometric center of the vehicle. Because the acceleration
force acts right at the tires and is parallel to the road surface, the
mass centroid is always located above the traction force vector. This
causes the car to lift on the front and squat on the rear whether it is
front, rear, or 4 wheel drive, during forward acceleration. This will
have the same affect as transferring weight from the front of the car
to the rear. When this happens, the rear tires will get a higher normal
force (weight applied) while the front tires will get less. This is referred
to as weight transfer.
If you design the car right, given the acceleration potential you have
you will set it up to just barely lift the front tires off the pavement
during maximum acceleration. This will apply all the vehicles weight to
the rear tires which will increase traction to its maximum. Adding weight
to the vehicle will reduce acceleration just as reducing power would.
In order to optimize your weight transfer, you can move your mass centroid
up. In other words, raise the vehicle height. If you get too carried away,
you will lift the front wheels too far on acceleration and loose control.
If that is the case, lower the mass centroid.
As you can see, front wheel drive is the last thing you want for drag
racing. Because of the weight transfer affect, you loose traction as you
increase acceleration on a front wheel drive vehicle. A rear wheel drive
vehicle will increase traction on acceleration.
The traction force on the tires is always parallel to the road surface
whether you are accelerating or cornering. Actually, cornering is just
another form of acceleration. Any change in velocity is acceleration.
Velocity is also a vector. This means it has a particular direction and
magnitude. Speed has a magnitude but not really a specific direction.
If you change direction of travel, you change velocity (but not necessarily
speed), thus you are accelerating. Cornering applies forces just like
forward acceleration. For cornering however, you want to lower your mass
centroid as much as possible to reduce body roll and keep more even weight
on all tires but more importantly to reduce the tendency to roll over.
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