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#1
08-06-2012, 07:45 PM
 powerhouse Senior Member Join Date: Mar 2011 Posts: 214
General Range Formula

Hey Guys

I'm working on a small school project and I need some help.

Basically, im creating a very simple range calculator in Matlab, a program maker.

I want to collect some small variables from the user,
Drag Coefficient
Frontal Area
Weight after conversion
Drive efficiency
Tire circumference
Rolling Resistance
battery pack kWh

I need to know how far someone can expect to go at 10, 20, 30, 40 mph etc.

I can't find a formula that incorporates drag and frontal area into finding range. I have tried reverse engineering existing calculators, but jeez they have so many variables its ridiculous.
Also, if any more variables are necessary, or certain ones arent let me know! I just have to figure out how speed is related to range.

Ultimately, I want the program to create a graph showing range vs speed. So the most important part is that I find out how speed is related to range.

Any help is appreciated!
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#2
08-06-2012, 07:55 PM
 major Senior Member Join Date: Apr 2008 Location: Ohio, USA Posts: 5,185
Re: General Range Formula

Quote:
 Originally Posted by powerhouse Any help is appreciated!
You calculate the power required for specific speeds.

The amount of time traveled at a specific speed gives you distance.

The time traveled using a specific power gives you energy.

So using the speed, power, time and energy, you can calculate the distance energy relationship.
#3
08-06-2012, 08:15 PM
 powerhouse Senior Member Join Date: Mar 2011 Posts: 214
Re: General Range Formula

Quote:
 Originally Posted by major You calculate the power required for specific speeds. The amount of time traveled at a specific speed gives you distance. The time traveled using a specific power gives you energy. So using the speed, power, time and energy, you can calculate the distance energy relationship.
Thanks major !!

I haven't taken physics yet so its all kinda new to me.

How do you calculate the power necessary at speeds? I think that would require the drag coeff and Rolling Resistance, but the problem is I don't know the formula that uses those!
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#4
08-06-2012, 08:19 PM
 TigerNut Senior Member Join Date: Dec 2009 Location: Calgary Posts: 277
Re: General Range Formula

Force times distance is work done (in the physics sense), this is equivalent to energy.
Force times velocity is power.

You'll have to work out, for each speed you're interested in, what all of the opposing force components are: air drag, tire Rolling Resistance, and gravity (if you're going up hills).

Air drag is proportional to the square of your speed, so you'll find that this starts to become significant pretty quickly. Rolling Resistance goes down slightly with speed, IIRC.

You can search out the appropriate conversion constants on Wikipedia, and there are tables of drag coefficients and frontal areas on ecomodder and elsewhere.
#5
08-06-2012, 08:30 PM
 powerhouse Senior Member Join Date: Mar 2011 Posts: 214
Re: General Range Formula

Quote:
 Originally Posted by TigerNut Force times distance is work done (in the physics sense), this is equivalent to energy. Force times velocity is power. You'll have to work out, for each speed you're interested in, what all of the opposing force components are: air drag, tire Rolling Resistance, and gravity (if you're going up hills). Air drag is proportional to the square of your speed, so you'll find that this starts to become significant pretty quickly. Rolling Resistance goes down slightly with speed, IIRC. You can search out the appropriate conversion constants on Wikipedia, and there are tables of drag coefficients and frontal areas on ecomodder and elsewhere.
Looking for some formulas, kinda tough

EDIT: I have found a somewhat useful formula

F= (mass x gravity constant x coeff of Rolling Resistance) + ((density of air x coeff of drag x frontal area x (velocity of vehicle)^2) / 2) + (mass x acceleration)

This is for flat surfaces
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Last edited by powerhouse; 08-06-2012 at 08:42 PM.
#6
08-06-2012, 08:40 PM
 major Senior Member Join Date: Apr 2008 Location: Ohio, USA Posts: 5,185
Re: General Range Formula

Quote:
 Originally Posted by powerhouse Looking for some formulas, kinda tough
It is not unique to EVs. It should be many basic vehicle performance books or papers or lecture notes. I took a look and was surprised it wasn't in this site's wiki.
#7
08-06-2012, 08:51 PM
 powerhouse Senior Member Join Date: Mar 2011 Posts: 214
Re: General Range Formula

Quote:
 Originally Posted by major It is not unique to EVs. It should be many basic vehicle performance books or papers or lecture notes. I took a look and was surprised it wasn't in this site's wiki.
Yeah, I searched diy before I even made the thread. Nothing much on the topic unfortunately.

Using the formula I posted above for force, how would you find power?
__________________
Check For Updates on the S2000!
http://electrichonda.blogspot.com/
#8
08-06-2012, 08:52 PM
 TigerNut Senior Member Join Date: Dec 2009 Location: Calgary Posts: 277
Re: General Range Formula

Quote:
 Originally Posted by powerhouse Looking for some formulas, kinda tough EDIT: I have found a somewhat useful formula F= (mass x gravity constant x coeff of rolling resistance) + ((density of air x coeff of drag x frontal area x (velocity of vehicle)^2) / 2) + (mass x acceleration) This is for flat surfaces
That should give a pretty good first approximation. Most likely it will give at least a 95% accurate answer, and some of the error will be due to errors in the vehicle mass, drag coefficient, or frontal area.
#9
08-06-2012, 09:08 PM
 major Senior Member Join Date: Apr 2008 Location: Ohio, USA Posts: 5,185
Re: General Range Formula

Quote:
 Originally Posted by powerhouse Using the formula I posted above for force, how would you find power?
Quote:
 Originally Posted by TigerNut Force times velocity is power.
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#10
08-07-2012, 02:51 AM
 PStechPaul Senior Member Join Date: May 2012 Location: Cockeysville, MD 21030 Posts: 1,180
Re: General Range Formula

I just made a web page using JavaScript that calculates force and power from the equations above. However I probably don't have the units correct, so please check it out and let me know what typical values are and the units so it will be correct. I can also add other common EV calculations, such as the Torque-HP-RPM formula and wheel RPM to speed. I can jazz it up with English/Metric conversions as well.

http://www.enginuitysystems.com/ForceCalculator.htm

I also put a link in the Wiki.

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