In this video we are going to look at drag force on irregular shapes, and in this case.
What we are going to do is look at a truck.
So we have four drivers and they were bored one day, with there routes.
So they made a wager.
They wanted to know if they had a distance of 500 miles, which one would spend the least
money on gas.
So how do we calculate the money spent on gas?
Well that is the required energy divided by the energy density, and that will give us
the amount of gas.
That is needed.
So how do we find the required energy?
Well the required energy equals the force times the distance divided by the energy of
efficiency.
So what force we are looking for?
This is the drag force, which is 1/2 times the coefficient of drag times the density
of the fluid, times the velocity squared times the frontal area.
Well in this particular the 1/2 of course is going to be the same the rho is going to
be the same because it is all air.
The frontal area of the trucks.
We will assume that they are all driving the same truck.
They will be the same.
The efficiency is going to be the same and the distance is going to be the same.
So actually all we have to do.
Is calculate the drag coefficients times this U^2 of velocity squared.
To find out which one uses the least amount of gas.
So lets go ahead and do that, and truck one it is going 60 mph, there is no head wind,
and it has a drag coefficient of 0.96.
Our second truck is also going 60 mph with no head wind.
However, what it has is a fairing, which is a piece that goes on top, and makes this truck
more streamline.
So it has a lower drag coefficient.
The third truck with no head wind, but this not only has a fairing.
It has a gap seal as well, which connects the fairing to a trailer and makes even more
streamline.
So its coefficient is 0.70.
Truck four, however, has a couple of issues.
It is going 80 mph.
It has a head wind of 25 mph.
It has a fairing, but no gap seal.
So it has a drag coefficient of 0.76.
Lets calculate this Cd times U^2 for each one of our trucks.
So the first thing we have to do is change mph into ft/s.
So 60 mph.
we multiply that by 5280 ft, because that is how many feet there are in a mile, and
1 hr is 3600 second.
So that is 88 ft/s.
So that is going to be our velocity for trucks 1, 2, and 3.
When we do truck four.
We have to take into account not only the changes in actual velocity, but the 25 mph
head wind.
So the velocity that is going to be used to calculate our drag force is actually 154 ft/s.
So now lets calculate that Cd times U^2.
So when we do it for truck one our Cd times U^2 equals 7434 and that is with a drag coefficient
of 0.96.
Truck two is 5885, and remember this is all for Cd times U^2.
So that drag coefficient that lower one by the fairing.
Lowers our Cd times U^2.
Four our third truck, because of the gap seal.
This goes down even further.
However for truck number four.
Even though it has a fairing, its Cd is 0.76.
The fact that it has 154 ft/s to overcome.
Gives a Cd times U^2 of 18024.
So this is going to use the least gas.
So we will call this 1.
This will be the next.
This one will be the next.
Finally truck four is going to use the most amount of gas.
So if want to find out exactly how much gas is being used.
We can set up a table.
So our table is going to consist of our drag force.
Which is in units of lbf.
Our energy, which is in units of ft*lbf.
Our required energy, where we have to take into account the efficiency, and this is going
to be in ft*lbf, and finally the amount of gas, which is going to be in gallons.
We are going to look at truck one, truck two, truck three, and truck four.
Remember that our distance is going to be 500 miles.
In addition, our efficiency is going to be 40 percent or 0.40.
Our frontal area is going to be 8 times 12 ft, or 96 ft^2, and our energy density is
going to be 9.47 times 10 to the 7th lbf per gal.
So when we use these numbers we end up with for the first one.
With a drag force of 849 lbf.
An energy of 2.2 times 10 to the 9th.
Our required energy is 5.6 times 10 to the 9th, and you are going to require then 57.6
gal for our distance.
When we fill in the numbers for the rest, and they follow this pattern that we see for
our Cd times U^2.
So this is 1.8 times 10 to the 9th, 1.6 times 10 to the 9th.
So the energy required is going down.
Until we come to truck four.
When we come to required energy.
Again it is going to go down for truck 2 and 3.
Again go up four truck four.
Finally when we look at these gallons of gas.
Which is really the most important thing, because we are talking about money goes down
to 45.7 gal, 42 gal, and our last truck is going to be 140 gal.
One thing to look at is the difference in adding our fairing from here to here is very
large, and compared to actually adding a gap seal.