| From: | Amonchare <mak9@******.EDU> |
|---|---|
| Subject: | max. speed |
| Date: | Fri, 12 Feb 93 21:38:16 EST |
How this doesn't get to envolved for any of you. I got the intermediate
equations from my college physics book. If it does page the end of the post
for the final formula. You find it surprisingly simaliar to the old one.
First I started with an engine of given power P in units of watts. The one
watt can also expressed as 1 (newton * meter)/second. A newton is a unit of
weight and can be expressed as one kilogram * acceleration Remember that a
kilogram is a unit of mass not weight. So that so far we had:
Power(w) = mass(kg) X acceleration(m/s^2) X velocity(m/s)
Since we are talking about a maximum velocity we can assume the power of the
engine is equal to the power neccessary to keep the vehicle moving at that
velocity.
Mass is easy to remove from the right side of the equation. Simply devide
both sides by mass of the total vehicle.
Power(W) mass(kg) x acceleration(m/s^2) x velocity(m/s)
-------- = -------
mass(kg) mass(kg)
the result is:
Power(W)
-------- = acceleration (m/s^2) x velocity(m/s)
mass(kg)
Accelaration in this case is the acceleration the engine must provide to
counter attack the decceleration forces acting on the car. There are many
different forces acting in this way. Wind resistance or drag is a major one
at high velocities. This force can vary from day to day. It depends on
whether you have a tail wind or a head wind, but general increases with speed.
Also this effect can be reduced by "streamlining" the body of the vehicles.
Among some of the other decceleration force is the friction with the road.
Anyway since the actual value of this acceleration is very complicated to
determine I suggest that we use a fixed average value; At least for cars.
Anyway by dividing both sides of the equation by an accelerate ( what ever the
value is) we get:
Power (W) Acceleration(m/s^2) x velocity (m/s)
----------------------------- = --------------------
mass(kg) x acceleration(m/s^2 Acceleration(m/s^2)
or
Power(w)
velocity (m/s) = -------------------------------
mass(kg) x Acceleration(m/s^2)
This is our maximum velocity.
Now lets see if we can make the equation fit a couple of cars. First we got
to assign some values to some of our varibles. First lets start with a luxry
sedan ie a large car no heavy accessories( armor, more body). Mass of these
cars are about 1500 kg in 1993. I believe that with new techinology and light-we
ight
composites of SR this can be reduced to 1300 kg or less. Lets stick with 1300 k
g.
I think Hayden was a little 3000 kg (3.3 tons). This means we have adjust the
car chassis table. Anyway thats mass.
Now engine power. In the same type of cars in power rating s of the
engines range from 100 to 120kw (130-165 hp). Sportier types have more power
but we want to talk average so lets use 110kw.
lets set acceleration equal to one to see how close we get to a
satisfatory answer.
110,000 w 3600 s/h
velocity= ------------ = 84.6 m/s x ------------ = 305 km/h
1300 kg x 1 1000 m/km
cruising speed would be 102 km/h
That worked well let's try another this time a small coupe
mass= 800 kg (1760 lb)
power= 65 kw
again acceleration =1
65,000 w 3600 s/h
max velocity = ------------- = 81.3 m/s x ----------- = 293 km/h
800 kg x 1 1000 m/km
cruising speed of 97.5 km/h
These are the only two examples I tried so far but these two work well,
fianally. Try it out see what you think. Oh, an d disregard my last post
this replaces velocity rules and i found a flaw in the economy equation and
I'm not sure how to convert power into NPU's. I'll work on this and get back
to you unless someone beats me to it.
Oh and here is the kph version of the max velocity formula condensed
power * 3.6
max velocity (kph) = -----------------
mass
-------------------------------------------------------------------------------
Guak
A.K.A. Amonchare
(Michael A. Kauffman)
mak9@******.edu
-------------------------------------------------------------------------------
