Horsepower
and Drag
Low fuel mileage for motorcycles
versus cars.....ETC.
© Copyright, 2011, R. Fleischer
hp-drag.htm-64
Some of you have made inquiries about whether or not modifications you are making really increase horsepower and/or torque. How much does it take to make any REAL difference on a practical basis? Why does a motorcycle get such lousy mileage compared to some cars which are vastly bigger and heavier? The following will discuss coefficient of drag and horsepower requirements, etc.
The Coefficient of Drag (Cd), is a huge
determining factor on performance as speed increases, as it
is NOT a straight-line function; which everyone
thinks it is from looking at only ONE of the two formulas
that are involved with drag and horsepower needed. Cd is a
complicated thing to measure without a wind tunnel or some fancy computer and
graphics work. Cd is not very usable for anyone but an
engineer. Motorcycles have a very high Cd, and hence get lousy gas mileage
compared to a car, even worse in comparison, considering the weight and size difference.
Sometimes folks ask questions about
RAM air
possibilities for no-cost supercharged horsepower.
Dynamic air pressure by or on a moving object are treated by
engineers as a certain size of flat plate moving through the air
at some speed. Dynamic air
pressure is proportional to the SQUARE of speed, but the horsepower to attain
that speed goes up as the CUBE of that speed change.
Think about that! This means that for oncoming air, just
the SPEED change, is proportional to the cube of gasoline usage.
Consider your Airhead moving at 68 statute
miles per hour. That is easily converted to feet per second, and the value
is 99.7, let us just say 100 feet per second. There is about 12
pounds of pressure per square foot of surface area. At 200 feet per
second (about 136 miles per hour) the pressure is 48 pounds per square
foot. (see, I did the calculations for you!!). Thus, the drag is 4
times higher for a doubling of speed. If one was to
divide by 144, you would have the pressure per square inch, in
this case 0.33. That is basically almost nothing compared
to atmospheric pressure forcing itself into the cylinders (about
15.0 psi at sea level). Thus ram-air supercharging effect
is nil until speed gets VERY high. It starts to make some reasonably
usable difference around 150 mph. Thus, ram air pressure does NOT
help at ordinary road speeds. AND, no, 'big scoops'
don't
increase that pressure and performance due to the mathematics and area
involved.
1. Several methods of proving performance increases come to mind. The best testing is on a dyno (dynamometer)....with the temperature and humidity of the incoming combustion air being measured and written down and accounted-for. Dyno's cost $3K upwards, and are expensive to rent. But, they are really great...especially if you use the same dyno for all testing.
2. The second best is often a top speed run. This works when the modification to the engine...or body work for streamlining, etc.,...is increasing top speed. You can compare, before and after. You could even do calculations based on the actual measured increase in top speed, to get an idea of the real Cd. Some folks do modify engines and other items just for snappier mid-range. A top speed run (besides the cops problem) should be run in both directions, and you should keep track of the outside temperature...which has a bigger effect that you might think; the humidity is much less important. It is fairly important to do this test on the same road surface each time, with same tire pressure, same equipment (air friction, etc., losses).
3. A speed run up a slope can tell you much, and it often can be done at legal speeds. Typically this is done on a slope that allows, let us say, third gear and 6000+ rpm or so...and the slope won't allow any more speed. This is one of my preferred methods. I also often use this sort of test to determine mixture, reading spark plugs or exhaust gases.....etc.
4. Acceleration testing can be done with a stop watch, over different speed ranges, and sometimes offers some decent measurements. Unfortunately, for JUST the drag-race start method, there are a lot of variables to consider. It generally is a poor method, unless you can have tight control over things. Where it CAN work out reasonably well, is a roll-on test, from a given rpm/speed in a given gear.
5. In the United States, horsepower means "Imperial" horsepower. The original description is the power a horse exerts in moving 550 pounds of something, one foot, in one second. It can include just the horse and its own weight. Horsepower can be defined many ways. Just one such is that 746 watts is one horsepower.
The term
brake horsepower (BHP) came from the measuring of horsepower
by a device that is called a water brake. A 'brake' loads the
engine...and the twisting force, called torque,
is then measured. It can be measured directly, with such as strain gauges,
or indirectly. In any event, BHP is
crankshaft measured power, unless specified at some other point, such as
transmission output or rear wheel output. Today, hydraulic brakes, water brakes,
electrical brakes...etc....are all in use. Typically we have some sort of
turbine...and a means to adjust characteristics, such as amount of
loading. Shaft horsepower is
NOT the same thing. It is supposed to mean
BHP, less
certain losses. In practice....especially decades ago...with the puffed
(advertising inflated) horsepower claims of car manufacturers, horsepower
was measured at the crankshaft, often without alternators, water pumps,
etc......all the power draining devices were eliminated...and sometimes
some real cheating was done...like measuring power at unlikely cold
temperatures, ....even using different air pressures, no exhaust back
pressure or optimizing the exhaust system for best extraction and input
characteristics....and changing the coolant temperature to non real world
temperatures.
6. There is a simple formula to calculate BHP:
BHP = 2 times pi times torque times
revolutions; all this divided by 550.
Pi is 3.1416 and torque is in pounds-feet, and revolutions are revs
per second NOT MINUTE!.
Obviously, we can change the revs to revs per minute, easily!
Here's another version:
P = 2
time pi times torque times rpm times 1.34 times 10 to minus third
power. Divide the results by 60.
For this formula P is in horsepower and torque is in Nm
7. Today, SAE (Society for Automotive
Engineering) specifications do not allow for the big inflated
values from the 60's and 70's. SAE standard conditions are 29.61 inches of
pressure of mercury atmospheric; 81 degrees Fahrenheit incoming air
temperature; and 60% relative humidity. These are real world
numbers.
There are other types of measuring standards. You may have
heard of the ISO international standard...often seen on threaded fastener
spec's. ISO for horsepower is similar, but not measured exactly the same
way as SAE, but it is only a couple of percent different (higher).
8. Note that both Imperial and
metric power can be expressed, and often is (see BMW spec sheets)
as Kw (kilowatts). Metric horsepower is now
larger than Imperial...since we are now measuring in the real world....but
not always...some fudge factors exist....I am speaking theoretically here
on metric hp being larger than Imperial. You can usually assume that
metric power times 0.986 gives Imperial. You can calculate KW into
Imperial, by dividing by 0.746.
9. I won't go into it deeply here....many folks HATE math and formulas...but you probably have noticed that you CANNOT separate a torque effect from a horsepower effect, and vice versa, due to that formula in #6. above. Because of the formula, and some other things, there is a place on every torque and horsepower curves chart [where both curves are shown], where they CROSS-OVER. It is ALWAYS at the same RPM. You cannot separate the interrelationship: if you change one item, at least one other is changed... torque times rpm is horses!!!
10. Those of you with some sudden
insight, might have noticed...or are asking...what happens if there is NO
rpm...the piston has not moved...does this mean torque and power are now
equalities within the equation? I just thought I'd drop that
in here...and let some old time steam engine enthusiasts have a tad of
fun.
I hope this clears a few things up. I am leaving the bit about the curves
crossing-over at a specific point, for those of you who are inclined
to do so, to try to think about why.
Revisions:
01/16/03: minor
clarifications, minor formatting and emphasis.
04/13/2003: add .htm title; minor clarifications
10/05/2003: Add note on Cd
02/25/2005: add copyright, better ID, clarify and upload
05/05/2005: expand #6
06/09/2011: Clean up. Rename. Same ID
of article number
© Copyright, 2011, R. Fleischer
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