Exploring Air Pressure: Calculating lbs of Force on a Vehicle at Sea Level

[Mech Cb]

Weight of Air Pressure...

How much air pressure (in lbs) is being exerted on the front of a vehicle per MPH it travels? I know all vehicles are shaped differently, so we'll focus on the license plate.

-No headwind, tailwind or any other wind
-Vehicle is traveling at sea level
-Vehicle is traveling in a straight line on a level surface


I'm basically just wanting to know what it would be before you start factoring in all the other elements.

 

[Ranger Mike]

the force it takes to push something thur air is usually calculated as aerodynamic DRAG
Aero drag = 1/2 DVA ²
where D is air density
A is frontal area
V is velocity
for real body shapes, air at standard conditions, V in MPH and drag is pounds of force this equation becomes
Drag= 1/391 Cd AV²
a slippery road car has a Cd of about 0.32
a chunk one is about 0.38

 

[rcgldr]

The dynamic pressure of the air is related to the acceleration of the affected air to the same speed as the license plate. The total pressure of the air at the license plate is the static pressure of the affected air plus the dynamic pressure and this total pressure is called the stagnation pressure.

http://en.wikipedia.org/wiki/Dynamic_pressure

A pitot static tube on an aircraft measures air speed by comparing stagnation pressure to static pressure.

http://en.wikipedia.org/wiki/Pitot_static

Note that most of the drag on a vehicle is due to acceleration (both linear and angular (turbulence)) of the air aft of the vehicle, due the low pressure "void" that follows the vehicle.

 

[Mech Cb]

Oh wow-that is WAY more complicated than I thought it would be! haha! So basically, would I be safe assuming that it depends on the momentum of the vehicle which in turn depends on weight?

 

[rcgldr]

depends on the momentum of the vehicle which in turn depends on weight?

The vehicle isn't being accelerated, but the air is. It's the momentum of the air that matters.

 

[Mech Cb]

But if the air is not moving(no headwind or tailwind), how does the air have momentum?

 

[Bob S]

You are much more unlikely to make mistakes if you do your problem in MKS.
I will give you specific numbers below

P = (1/2) C_p rho A v³ (watts)

where
C_p = 0.32 (unitless ; drag coefficient)
rho = 1.29 (Kg/m³; density of air, sea level, 20 deg C)
A = 2.5 (m²; frontal area of vehicle)
v = 25 (m/sec; velocity)

Thus
P = (1/2) x 0.32 x (1.29 Kg/m³) x (2.5 m²) x (25 m/sec)³
P = 8062.5 Newtons x meters/sec
P = 8062.5 joules/sec
P = 8062.5 watts

Note that P scales as velocity cubed.
Review units to verify that this has dimensions joules/sec

 

[Mech Cb]

Jeff, I think i know what you're talking about now-you meant the air is being moved by the object moving through it, correct? So then the aerodynamic drag being spoken of by Mike is the resistance of the air. I learned that back in jr high watching NASCAR and learning about drafting, but for some reason, I forgot all about that. As far as a mathmatical equation, Bob, you completley lost me! But I think that's because I'm just trying to process too much at once. I'm going to go get some reaserch from weatherchannel.com about my local area, and then get some figures on a 95 Freightliner steak-truck and a 99 Saturn sc1. I think once I have more info on those two vehicles and avg driving conditions around St Marys, GA I'll be able to focus better on the equations.

 

[Cyrus]

You can't look at the pressure on the liscence plate void of the geometry of the vehicle behind it. The stuff behind the car affects the pressure upstream of it.

 

[Bob S]

As far as a mathmatical equation, Bob, you completley lost me! But I think that's because I'm just trying to process too much at once. I'm going to go get some reaserch from weatherchannel.com about my local area, and then get some figures on a 95 Freightliner steak-truck and a 99 Saturn sc1. I think once I have more info on those two vehicles and avg driving conditions around St Marys, GA I'll be able to focus better on the equations.

The mass of air is about rho = 1.29 kilograms per cubic meter (sea level, 68 deg F). If the vehicle had to push on and accelerate 1 cubic meter of air to the velocity of the vehicle, the energy would be (1 kilogram-meter²/sec² = 1 joule)

E = (1/2) rho v² joules per cubic meter.

If the vehicle had a frontal area A and velocity v, then the vehicle displaces a volume A (meters²) times v (meters/sec) = A v cubic meters per second. Then the power to push the air aside would be

P = (1/2) rho A v³ joules per sec (watts).

Note the velocity cubed dependence. Careful aerodynamic design can reduce the air drag, leading to a coefficient of drag C_d, leading to the power being

P = (1/2) C_d rho A v³ joules per sec (watts).

The measured drag coefficient also includes the effect of the vacuum behind the vehicle, and the turbulence of the air, so it may actually be velocity dependent.