Tool for visualizing aero vs rolling resistance - Gas Savers

krousdb · 03-18-2006, 08:33 AM

I have developed a spreadsheet that shows the contribution of aero drag and tire rolling resistance versus speed. I used the formula in the last post to this thread:

http://www.gassavers.org/forum_topic...reduction.html

Just enter your values (numbers in blue) and it will calculate aero and RR and also will calculate a theoretical MPG. Of course there may be an error in the calcs, but the MPG numbers seem to make sense. One caveat is the ICE efficiency. I set it up to show the same efficiency at all speeds which is not an accurate representation of reality. you can enter a separate efficiency for each speed to be more accurate, although it is really just a guess.

Anyway the point is not to calculate MPG, but rather to see how your CD and tire RR contribute to total drag at a given speed. You can simulate weight reduction, change in frontal area, CD and tire RR. Maybe it can help figure out the best place to spend your time/money.

Now if only I could figure out how to host a spreadsheet. Here is a jpg anyway...
http://img99.imageshack.us/img99/398...adsheet3ls.jpg
http://img206.imageshack.us/img206/4598/aerovsrr6yp.jpg

SVOboy · 03-18-2006, 11:00 AM

Email it to me and I'll host it or talk to Matt and he can prolly host it also. Looks very much on the cool side, can't wait to play with it, thanks a bunch,

Matt Timion · 03-18-2006, 11:45 AM

What I like about this is that it shows target areas based on what you want to accomplish. For example, if you primarily drive around town, (under 35mph) you are better off getting LRR tires. If you drive over 35mph on a regular basis, aerodynamic modifications will yield the best results.

krousdb · 03-18-2006, 12:27 PM

SVOBoy is hosting it here. I'm sure that it can be improved upon.

http://www.geocities.com/frontsidesk8er/delsolaero.xls

A few more bits of info.

The CRR number is tire RR plus other mechanical losses. The 0.008 value is a good guess for LRR tires at 40 PSI based on the thread I referred to earlier. The CD and FA should be available on google for your car. The default fuel value is for summer fuel, 114,500 BTU converted to Watt hours. Winter fuel is 112,500 BTU and E85 is 80,000 BTU. Just google the BTU to kWh conversion to get the appropriate number to plug in.

The MPG figures are just based on the fuel energy content times the efficiency of the engine. The fuel value is well known but the engine efficiency changes based on RPM I would guess. The engine efficiency should be the highest and fairly flat between the torque and HP peaks. Based on my 55 MPH testing last week, a 26% efficiency with winter fuel gives me 57 MPG at 55 MPH, which is about what I got in my testing. The efficiency number sounds high, which might be an indication that the CD is lower than .378 or that the highway hypermiling technique, 50 - 60 MPH, accel down hill, bleed off up hill, effectively increases the engine efficiency.

As a comparison, I plugged in the weight, CD and FA for SVOBoy's Torino Rex and got 70 MPG at 55 MPH, 13 MPG better than with the Del Sol.

MetroMPG · 03-18-2006, 12:48 PM

awesome spreadsheet - thanks. this is crying out to be made into a web page form. javascript anyone?

too bad it doesn't include a temperature variable which would show its effect on drag numbers (both aero and tire/mechanical).

SVOboy · 03-18-2006, 12:57 PM

Quote:

awesome spreadsheet - thanks. this is crying out to be made into a web page form. javascript anyone?

I'll try my hand with some java later.

And dan, sorry about the whole my car being a more efficient base thing, I'm sure I'll find a way to make it get bad gas mileage still.

MetroMPG · 03-18-2006, 01:00 PM

i'll fire this into a coldfusion page later on today too. but right now i'm going outside to play with my forklift while it's still light out.

(no motorectomies today - we broke the jack handle! but there's other stuff i can still take apart...)

krousdb · 03-18-2006, 01:26 PM

Quote:

Originally Posted by MetroMPG

awesome spreadsheet - thanks. this is crying out to be made into a web page form. javascript anyone?

too bad it doesn't include a temperature variable which would show its effect on drag numbers (both aero and tire/mechanical).

Well actually with a little work we can. The RHO value has to do with the density of air at sealevel. Some googling should give us different numbers to plug in as they relate to temp and altitude. No time right now, maybe I will try later.

Matt Timion · 03-18-2006, 02:39 PM

If you make this into a web based spreadsheet I'll happily host it here. I've been thinking of adding a section of the site for "online tools." This would be perfect for such an area.

MetroMPG · 03-18-2006, 08:33 PM

http://metrompg.com/tool-aero-rr.htm

i left out (in the output) some of the fields that are constants. still need to add some form field / table column descriptions, credits & links.

feedback ?

Matt Timion · 03-18-2006, 09:16 PM

Quote:

Originally Posted by MetroMPG

http://metrompg.com/tool-aero-rr.htm

i left out some of the fields that are constants. still need to add some form field / table column descriptions, credits & links.

feedback ?

Looks good to me. What was it written in? Java? Any chance you want to give me the source code so I can post it up here? Credit will be given, of course.

MetroMPG · 03-19-2006, 07:16 AM

it's coldfusion. i was going to do a javascript version, but i'm faster with CF (though javascript would have had a portability advantage). i can zip the file and PM you a link to download it. you can translate it to php or whatever suits you.

but let's just wait for a bit of feedback first. no point in both of us revising the same code at the same time.

also, i should compare the formulas used against another set i've seen.

krousdb · 03-19-2006, 07:18 AM

Quote:

Originally Posted by MetroMPG

http://metrompg.com/tool-aero-rr.htm

i left out some of the fields that are constants. still need to add some form field / table column descriptions, credits & links.

feedback ?

If you are so inclined, see http://en.wikipedia.org/wiki/Density_of_air

FE increases as the density of air decreases which happens with increasing temperature, increasing humidity, increasing elevation and decreasing barometric pressure. I could have figured this out 15 years ago but my brain hurts when I look at it now. At least there is a table of density vs temp. You could try to fit a curve to it if you can't figure out the formula.

MetroMPG · 03-19-2006, 05:27 PM

Quote:

If you are so inclined...

well, i was *partially* inclined.

i updated the tool with the table data from wikipedia, so you can select from a range of pre-calculated rho (air density) values based on various temperatures. the table doesn't specify the other values used in the rho calculations, but i suspect they used "standard" values for pressure & water vapour content (humidity).

http://metrompg.com/tool-aero-rr.htm

while roaming around the web reading about this, i came across a very interesting page which actually does the rho calculation (javascript) from input values of air temp, absolute pressure, and humidity.

most interestingly, it then takes that info and calculates *relative engine HP*.

since our cars' engine hp figures are calculated by SAE rules at standardized atmospheric conditions, this tool shows the effects on HP of different atmospheric conditions (as they affect density of the intake charge).

Quote:

For the SAE J1349 relative horsepower calculations, the standard reference conditions are: Air temp 77 deg F (25 deg C), 29.235 Inches- Hg (990 mb) actual pressure and 0% relative humidity.

http://wahiduddin.net/calc/calc_hp_abs.htm

krousdb · 03-19-2006, 05:45 PM

Nice, I suspect standard pressure and humidity values also. The temp selection works just fine the way it is. I think you might want to mention that this calculator is primarily for calculating aero drag and rolling resistance. The MPG calc is subject to lots of speculation about how one calculates ICE efficiency. MPG figures should be taken with a grain of salt. I backed into a 26% efficiency based on the highway testing I did at 55 MPH. At 26% that is very high compared to the 13% figure that I have seen for modern ICEs. But maybe the 13% is for normal driving through a whole tank, not at a constant speed.

MetroMPG · 03-19-2006, 06:29 PM

agreed - it needs to be fleshed out with disclaimers, variable desrcriptions, links to relevant info & credits.

added one more feature: a quick select for summer / winter fuel energy densities.

note that the temperature calculation doesn't have an effect on rolling resistance, where in real life it would (tire rr decreases as temp increases). the temp calc on my page only affects aero drag.

i have a couple of other simple additions in mind. i'll do them tomorrow.

MetroMPG · 03-19-2006, 06:39 PM

one other thing i noticed in the spreadsheet formula: tire drag is unchanging at all speeds (vehicle mass * CRR * gravity constant), but doesn't rolling resistance increase with speed?

(EDIT: my mistake; the spreadsheed doesn't show this; see below.)

i was looking at other sites, and saw this formula for HP to overcome tire/mechanical drag. it's more precise, and varies with speed:

Quote:

HP= V/375 times[0.01184 W + 0.000353(V-66)W].

Velocity V is in miles per hour,Weight W is in pounds.If your speed
is below 66-mph,then the second term within the parenthesis falls
out.Again,to get flywheel power, take your result and divide by
0.95. This yields Bhp the engine or electric motor must provide to the
powertrain, at 95% mechanical efficiency for the powertrain.

it would be nice to have a way to play with head/tail winds on the page as well. it shouldn't be too hard to revise the formula. i'll think about that a bit tomorrow as well - unless someone wants to jump in before then

krousdb · 03-20-2006, 03:33 AM

Yes, rolling resistance should increase with speed. Column U on the spreadsheet clearly shows that it does. The formula used was posted here by someone else and I cannot conform the tire resistance part. By all means, if you have found a better formula, you should use it.

Calculating the effect of a DIRECT headwind or tailwind would be easy, just add/subtract the windspeed to the aero part only. Calculating winds at other directions than 0 degrees and 180 degrees involves the side area of the vehicle and is much more complicated to do, if at all.

Matt Timion · 03-20-2006, 07:30 AM

Quote:

Originally Posted by krousdb

Calculating the effect of a DIRECT headwind or tailwind would be easy, just add/subtract the windspeed to the aero part only. Calculating winds at other directions than 0 degrees and 180 degrees involves the side area of the vehicle and is much more complicated to do, if at all.

ACtually this is very easy to do as well. All that we would be doing is solving for an unknown side of a triangle, which is pretty simple trigonometry.

MetroMPG · 03-20-2006, 09:21 AM

you're right krousdb. if you remove aero drag from the picture (by setting column M values to zero), you can see HP Tires continues to increase with speed. my bad.

when i compared the two different formulas for rolling drag, you get these figures:

MPH - HP TIRES (orig. formula) - HP TIRES (diff. formula)

05 - 0.261422561 - 0.398304667
10 - 0.522845122 - 0.796609333
15 - 0.784267683 - 1.194914
20 - 1.045690244 - 1.593218667
25 - 1.307112805 - 1.991523333
30 - 1.568535366 - 2.389828
35 - 1.829957927 - 2.788132667
40 - 2.091380489 - 3.186437333
45 - 2.352803050 - 3.584742
50 - 2.614225611 - 3.983046667
55 - 2.875648172 - 4.381351333
60 - 3.137070733 - 4.779656
65 - 3.398493294 - 5.177960667

the difference is consistent: 52% more drag in the 2nd formula at all speeds. maybe it reflects the difference between LRR tires and non-LRR tires.

if you want, you can enter a column with the new formula in Row 2: =A2/375*(0.01184*B2 + 0.000353*B2)

(it applies only up to 65 mph. for some reason, rolling resistance as calculated in the second formula is set to increase above 66 mph. i'll see if i can find out more about it.)

krousdb · 03-20-2006, 09:28 AM

Quote:

Originally Posted by Matt Timion

Quote:

Originally Posted by krousdb

Calculating the effect of a DIRECT headwind or tailwind would be easy, just add/subtract the windspeed to the aero part only. Calculating winds at other directions than 0 degrees and 180 degrees involves the side area of the vehicle and is much more complicated to do, if at all.

ACtually this is very easy to do as well. All that we would be doing is solving for an unknown side of a triangle, which is pretty simple trigonometry.

OK, and how do you find the CD and area for the side of your vehicle? That data is not published, nor is it measured that I know of.

MetroMPG · 03-20-2006, 09:30 AM

Quote:

ACtually this is very easy to do as well. All that we would be doing is solving for an unknown side of a triangle, which is pretty simple trigonometry.

i think what krousdb was getting at is crosswinds have additional effects beyond just figuring out the new apparent windspeed and adding it on to the vehicle speed. (calculating "apparent wind" using true wind and vehicle speed is common for sailing, using vectors.)

e.g. rolling resistance changes in a crosswind (but not in a tail/head/no wind). in a crosswind the tires scrub (you have to counter steer against the wind), and the amount of scrub depends on the particular aerodynamics of the vehicle (and the cross wind strength/direction)

krousdb · 03-20-2006, 09:33 AM

Quote:

Originally Posted by MetroMPG

you're right krousdb. if you remove aero drag from the picture (by setting column M values to zero), you can see HP Tires continues to increase with speed. my bad.

when i compared the two different formulas for rolling drag, you get these figures:

MPH - HP TIRES (orig. formula) - HP TIRES (diff. formula)

05 - 0.261422561 - 0.398304667
10 - 0.522845122 - 0.796609333
15 - 0.784267683 - 1.194914
20 - 1.045690244 - 1.593218667
25 - 1.307112805 - 1.991523333
30 - 1.568535366 - 2.389828
35 - 1.829957927 - 2.788132667
40 - 2.091380489 - 3.186437333
45 - 2.352803050 - 3.584742
50 - 2.614225611 - 3.983046667
55 - 2.875648172 - 4.381351333
60 - 3.137070733 - 4.779656
65 - 3.398493294 - 5.177960667

the difference is consistent: 52% more drag in the 2nd formula at all speeds. maybe it reflects the difference between LRR tires and non-LRR tires.

if you want, you can enter a column with the new formula in Row 2: =A2/375*(0.01184*B2 + 0.000353*B2)

(it applies only up to 65 mph. for some reason, rolling resistance as calculated in the second formula is set to increase above 66 mph. i'll see if i can find out more about it.)

Perhaps the RR increases over 65 MPH to reflect additional downward force due to aero drag which manifests itself as additional weight?

MetroMPG · 03-20-2006, 09:38 AM

Quote:

Originally Posted by krousdb

Perhaps the RR increases over 65 MPH to reflect additional downward force due to aero drag which manifests itself as additional weight?

i thought of that too, but then i think i've heard that most non-racing cars produce lift, not downforce, at highway speeds. which would mean a *lessening* of rr from reduced apparent weight. i'll look into this and get back.

Matt Timion · 03-20-2006, 09:58 AM

Quote:

Originally Posted by krousdb

OK, and how do you find the CD and area for the side of your vehicle? That data is not published, nor is it measured that I know of.

IN that case, it's not easy.

JanGeo · 03-20-2006, 10:07 AM

Ignore the side forces of the wind and just deal with the cosine of the angle times the wind velocity which gives you the frontal effects vector.

Matt Timion · 03-20-2006, 10:20 AM

Quote:

Originally Posted by JanGeo

Ignore the side forces of the wind and just deal with the cosine of the angle times the wind velocity which gives you the frontal effects vector.

That's actually exactly what I was thinking. An angled wind will just produce less of a frontal wind. I'm thinking that maybe all that can be done is ignore the side wind forces as it is impossible to really calculate.

krousdb · 03-20-2006, 10:57 AM

Quote:

Originally Posted by Matt Timion

Quote:

Originally Posted by JanGeo

Ignore the side forces of the wind and just deal with the cosine of the angle times the wind velocity which gives you the frontal effects vector.

That's actually exactly what I was thinking. An angled wind will just produce less of a frontal wind. I'm thinking that maybe all that can be done is ignore the side wind forces as it is impossible to really calculate.

A physicist friend of mine has developed a calculator for Prius MPG. As it turns out, crosswinds cause more drag than headwinds:

http://privatenrg.com/Crosswinds.htm#Crosswinds

The 70/30 rule is also interesting.
http://privatenrg.com/index.htm#WindAssistScreen

See all of his Prius related info here:
http://privatenrg.com/

JanGeo · 03-20-2006, 11:06 AM

Actually I have heard that you can ignore the CD Drag Coeffient at lower speeds (under 100mph) as it is such a small portion of the rolling resistance and frontal area drag as to not matter much. Hard to say without testing further - maybe a few foam shapes held out the window of a moving car on a spring scale (a poor mans wind tunnel) will test the drag effects at various speeds.

Took the xB out for some highway miles yesterday after I gggggggassed it up OUCH! glad I pay after I pump because I didn't expect it to take $25 to fill it up yikes - really should have filled it last week for a few bucks less. Anyway I was on a long down hill and pushed the pedal down and the gps registered 86.3mph in just a few seconds from 60mph. On the tight on-ramp coming back I opened it up in third to about 5500 rpm and then hit 4th for a little more then dropped it into 5th as the cars behind me started getting smaller - man this box really moves out! Kills the mileage for the day however only about 43mpg. HA HA HA HA HA was getting used to the high 40's.

MetroMPG · 03-20-2006, 11:46 AM

Quote:

Originally Posted by krousdb

A physicist friend of mine has developed a calculator for Prius MPG. As it turns out, crosswinds cause more drag than headwinds:

this makes sense when you think about it. vehicles are not at all aerodynamically optimized to be travelling "sideways" through the wind.