[Diy_efi] Area under torque curve?

[mrbeau0]

All,

Not to beat this to death, but there's another way of looking at this which
may help understand the difference between torque and HP.

We're interested in increasing the velocity over time (i.e. m/s^2).  This is
called the acceleration (or "a") of a vehicle.  The vehicle's energy (J for
joules) is proportional to it's mass times the velocity squared ( 1/2 * m *
v^2).  Assuming the mass stays the same, if you increase the energy of the
vehicle, you are speeding it up.  This change in energy happens over a
period of time, and the change of energy per unit time is the definition of
power (which is J / s).

So, if the vehicle accelerates from 10 m/s to 20 m/s in 2 s, and it weighs
1000 kg, what power did it take?

Easy:  .5 * 1000 kg * (20^2-10^2) m^2 / s^2
       ---------------------------------
                      2 s

=  75000 J / s  =  75000 W = 75 kW = ~100 hp

Notice torque isn't in here at all.  This 100 hp is the average power over
the acceleration period--if you have a CVT and it ran at one engine speed
point, it made 100 hp at that RPM.

You can also get here from F = m * a, but it gets confusing because you see
F for force and assume that force is coming from just the engine torque.
The problem is you need to look at the torque over time *at the wheels*,
which is really just power.  If torque was all that mattered, you'd see
people drag racing turbo diesels instead of their gasoline equivalents.  I
could have an engine that made 1000 ft-lb of torque and only 10 hp--it'd
launch pretty good at the strip, but It would be at top speed by the 60'
mark...  You might think an engine with 1000 hp and only 10 ft-lb would
never get off its mark, but geared appropriately (down from the 500,000 RPM
at peak hp...) the _torque at the wheels_ would be enormous and beat any
turbo diesel put up against it. :-)

Hope this helps.

Matt.


-----Original Message-----
From: diy_efi-admin at diy-efi.org [mailto:diy_efi-admin at diy-efi.org]On
Behalf Of Mike Diehl
Sent: January 2, 2003 10:53 PM
To: diy_efi at diy-efi.org
Subject: [Diy_efi] Area under torque curve?


Hi all.

I've been thinking....

If you have a plot of acceleration over time, then the area under that curve
is speed at a given time.  And the area under the "speed" curver over time
is
distance traveled at a given time.

Now, if you had a plot of torque over RPM, is there a similar interpretation
of the area under such a curve?  The reason I ask is that I know/read that
the area under the torque curve is a good/best indication of an engine's
overall performance.

--
Mike Diehl
'87 MR-2, 7A-Ge, Hand-bent headers
'96 4-Runner, Bone Stock
'90 Corolla, disguised as a Geo Prism.

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