Height values based off barometric pressure

[hurlbrrw]

Homework Statement

I'm doing research with a professor at my college this summer on energy modeling for an electric vehicle. We're trying to figure out a way to make a model to predict how much energy an electric vehicle would need in order to do a certain path, but that requires testing of pre-determined paths, so we're using a GPS unit, mostly for height values. The only problem is that modern day GPS units are not very accurate in the Z direction, so we're having trouble getting consistent slopes of the road. So we've made a pressure differential sensor that finds the difference of pressure from our original point. We can find out initial height fairly accurately, so we were hoping this would work more effectively.

The problem we're running into is actually getting height from our pressure. What is an equation that we could use in order to get change of height from our difference of pressure? We are also measuring temperature and relative humidity if that has anything to do with it.

Homework Equations

Equations I've found thus far searching on the internet:
p=p0(1-L*h/T0)^(g*M/(R*L))
where p0 is standard pressure, L is temperature lapse rate, T0 is standard sea level temperature, M is the molar mass of dry air, and R is the universal gas constant.

Also,
z = (RT/gM).loge(po/p)

The Attempt at a Solution

I think I've already mentioned this.

 

[Redbelly98]

Welcome to Physics Forums

Looks like your equation will work just fine. You should be able to use p0 and T0 at your starting reference point (where therefore h=0), and simply subtract p0 from p to get things in terms of pressure difference. Values for the parameters are given in the wiki article (which you have probably already seen):

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

By the way, have you already figured out how accurate your pressure difference measurement is? Pressure drops by 1% roughly every 280 feet in altitude. So you can get an approximate idea by using

$$p = p_0 (0.99)^{h/(280')}$$

where p₀ is the pressure at the starting point, and h is measured from that location. The equation will vary with temperature, but at least you can use it and the accuracy of your pressure readings to gauge the accuracy in h.

Perhaps others can chime in with a more accurate equation, or explanation of how to use the equation you gave.

p.s. I have moved this thread out of the Homework section, since a summer research project is not really considered homework. (And other forum members are freer to give you more help than if your post is in the Homework area.)

 

[klimatos]

The problem we're running into is actually getting height from our pressure. What is an equation that we could use in order to get change of height from our difference of pressure? We are also measuring temperature and relative humidity if that has anything to do with it.
QUOTE]

Your formula is the accepted one. Keep in mind that it is only valid under conditions of pure equilibrium. It will give erroneous results when the wind is blowing or weather is occurring.