Date: October 2002
We are a volunteer fire departmen dive team.We
recover stolen and dumped automobiles for the police department using lift bags. Is
their a way to compute the cubic foot displacement of an automobile?
This would assist us to determine the amount of cubic feet of air required to
lift the car.
This is difficult to determine very exactly because autos all have
different shapes. But here is how I would approach the problem: 1. You can
find out the weight of a car, truck, etc. by year/made/model either from
your state Department of Motor Vehicles or from the manufacturer. There may
even be a book tabulating this data. I don't know. 2. As a starting point
assume the vehicle is an ellipsoid of revolution. The volume, V(formula),
is: V(formula) = 4/3(pi)BA^2 where A = the length of the vehicle, and B =
For this calculation you can approximate (pi) = 3.1416 by "3" so the volume
V(formula) = 4BA^2. For each make/model/year that you recover you can
develop a data base of the actual displacement vs. the displacement
calculated from the formula V(formula) = 4BA^2 so add a
"correction factor = K" to the formula. Then: V(actual) = 4KBA^2 The ratio
V(actual)/V(formula) = K.
The hope is that V(formula) takes into account most of the volume, so that
"K's" will cluster around the same value. Keep a record of your recovery
history (or look back into the files and see if actual displacements were
recorded) to get a value for the factor "K".
I am not quite sure I understand the question. I think you are asking
how much the weight of the car is decreased when it is underwater due
to the buoyancy of the water displaced by the car. I can think of
several ways to determine the displacement of an automobile, but none
that would be very useful to you. One would be to lower the car into
a big pot and see how much the water level rises. Then the buoyant
force would be that change in level (in feet) times the area of the
pot (in square feet) times the density of water (62.3 lb/cubic foot.
Another way would be to hoist the car with a crane equipped with a
scale and see how much the weight recorded by the scale decreases as
the car enters the water.
Maybe the best way is to estimate the volume of water displaced by the
car (in cubic feet) and multiply by the density of water. Note that
if a bubble of air is trapped anywhere in the car (most notably,
perhaps, by the roof of the passenger compartment), the effective
weight of the car will be decreased by the volume of that bubble times
the density of water. Maybe the car manufacturer can give you a
reasonable estimate of the volume of water likely to be displaced by
an underwater car.
Wish I could be more helpful.
Best, Dick Plano
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Update: June 2012