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Old 01-29-2008, 11:43 PM   #1 (permalink)
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Aerodynamics Seminar # 6 - by Phil Knox

This post was originally written by Phil Knox (aerohead), and it first appeared on the MaxMPG group. Phil has done a lot of work educating the masses about the critical role aerodynamics play in efficiency, and has spurred many in the DIY crowd to take matters into their own hands.

This is the sixth in a series which I'm reproducing here with permission.


Go to: Aerodynamics Seminar index

---

Aerodynamics Seminar # 6 - by Phil Knox

(Note: Phil wrote this preface to #6 in a separate message; I think it's worth posting along with the #6 info. - Darin)


Preface

Hello all. As my Tuesday departure deadline approaches much remains to do. I have been collating materials for the "math" section of the seminars. It looks like it will be after I return from New Mexico before I can post the formulas I wanted to share.

There is much to complete on the T-100 and after I leave here tonight,its off to HOME DEPOT for more supplies and work into the night. Hurricane Rita could drop 4-5 inches on us and I have no idea what kind of "work" conditions I will have for fabricating. It was 102-degrees today,so again I'll cook well into the night.

The formulas,once posted,will allow everyone to calculate aerodynamic loads for any vehicle,knowing a few perameters. You'll be able to estimate road load horsepower for a vehicle at various conditions.With your own mileage numbers you'll be able to calculate your brake specific fuel consumption,estimate top speeds,fuel economy,range etc.

A pocket calculator will be handy.There is no trigonometry or calculus.Its all pretty much multiplication,division,and working with percentages.We'll walk through some examples together.No tests!!!!!!!!!!!!

If you do not presently have a "baseline" for your vehicle,you'll want to get a simple notepad for your vehicle and something to write with.I record: date, odometer reading, miles driven, fuel price, fuel cost, gallons, mpg, station,and any notes about modifications to vehicle, weather,etc.

By tracking mileage I can establish what the vehicle does with no modifications.When I make a change and see different results,I can use the formulas to quantify what if anything I've accomplished. If the vehicle performance changes for no reason,I can consider a tuneup or whatever. The main thing is "write stuff down!" If you know where you are and want to investigate if a modification might make sense, you can do it on paper and see if you want to proceed.

Long ago I wrote a simple program in BASIC and witha few keystrokes,could race through some calculations. Technology asside,for the day to day world we are basically looking at odometers and fuel pump readings. If you have an electric,you'll be working with kilowatts, power transfer efficiency, motor efficiency.Then,once your at the drive wheels, your down to rolling resistance and aerodynamic drag like everything else. If anyone has any specific questions, I'll try and get something for you.

When your looking at your car,think of a sailfish or perigrine falcon. Think of bottlenose dolphin and penguins. I was in a category-5 hurricane today and thought little of it. At 150-mph the Piper Cherokee I was flying in was right at home with this kind of wind loading. All the ample radii and gently sloping surfaces of the Cherokees air frame gave the air nothing to grab hold of.

As John G. mentioned in his blog,If I encounter headwinds on my trek next week, I'll easily be driving in a Class-1 hurricane. The aero mods to the T-100 hopefully will allow me to pass without incident.

I won't worry about my home as it is also aerodynamic, a ferro-cement dome which a tornado would shy away from and tidal surge,while wet,would eventually abate and leave me relatively unscathed.

Wish me well and I'll catch up in a couple of weeks, Phil.

Seminar # 6
(Note: Where Phil refers to photos/images in his text, I intend to come back and post them once all the Seminars are online. - Darin)

Hellow all. I had hoped to post large,neat,formulas in the photo section of the site. I think everyone needs these sooner than later so here goes.

The horsepower it takes at the drivewheel of your vehicle to overcome aerodynamic drag can be estimated by the formula
HP =V/375 [ 0.00256 X Cd X A X (V squared)]
where V= speed in miles per hour, Cd is your drag coefficient,A= frontal area of your vehicle,and (V squared) is your speed times itself.

Frontal area can be approximated by multiplying your vehicles width times its height,times 0.84. Frontal area is in square feet, so as dimensions are usually given in inches,divide the result by 144 to get square feet.

After you get the result,you can obtain flywheel horsepower by dividing your HP by 0.95 which yields Brake horsepower(Bhp).

These numbers are for standard barometric pressure, no wind, dry road, no more than 0.5% grade, 60-degrees F.

If you don't have frontal area,estimate it. Plug in your drag coefficient,and speed,multiply everything inside the parenthesis together,then multiply all that by your speed again and finally,divide by 375.

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Old 01-30-2008, 05:31 PM   #2 (permalink)
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Ummm... airplanes don't know what windspeed is unless they're interfacing with the ground!
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Old 02-29-2008, 09:18 AM   #3 (permalink)
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Calculating Horsepower requirements - including weight

Understanding that HP to overcome aero/drag is helpful. I want to include vehicle weight in my calculations to fully understand the impact of weight.

I came across this, but didn't get to an understandable value. I may just be overlooking some error in my calculations.
Pmotive=1/2*Cd*A*rho*v^3+Crr1*m*g*v
from http://www.geocities.com/greglocock/

My attempt at this calculation is attached on the second tab. Please let me know if anyone can fix it or provide the conversion from Pmotive to HP (or if you have a better spreadsheet). The first tab has the calculation from this discussion (The results look correct to me).

With significant investment, I think I can lower my weight by 200 lbs. Hopefully I can get some idea of the pay back. Spending most of my time at a stead speed (70 mph), I expect less pay back than the average vehicle. Taming my driving habits has already given me a 10% improvement (from average of 27 mpg to a max of 31.5).

I also want to find [easy] ways of reducing my RPMs at highway speeds from current 2750 to about 2200, but that's a different topic...

Thanks.
Attached Files
File Type: xls HP_requirements_calculations.xls (22.5 KB, 36 views)
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Old 02-29-2008, 09:29 AM   #4 (permalink)
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Let's stick to the metric system since it seems to use it, mostly?

1/2C_d is unit-less
A in m^2
rho is density, so kg/m^3
v is m/s, so v^3 is m^3/s^3

so we have kg*m^2/s^3
1 N is kg *m / s^2 -> Nm/s
1 J is Nm -> J/s
1 W is J/s, so we are left with pure watts
1 hp is 0.7457 kW

Essentially we take the result of the first part and *10^-3 / 0.7457, or multiply by 0.01341.

I'm not sure what the second part of the equation is, the addition, but in order to add numbers, the units MUST match. Pmotive=1/2*Cd*A*rho*v^3 is normal for a flat surface. What is Crr1?
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Old 02-29-2008, 10:12 AM   #5 (permalink)
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Quote:
Originally Posted by Frank Lee View Post
Ummm... airplanes don't know what windspeed is unless they're interfacing with the ground!
I'm no expert on this (only been in a co-pilots seat 2 times) BUT Pilots can calculate wind speed (at their altitude). The first plane I flew (piper Cherokee 180) did not have GPS and relied upon the tower to give a radar ground speed and heading, we then (re-)calculated out flight plan based on the wind speed/ direction. Plane #2 Cessna (rental) had a GPS which interfaced with the majority of the avionics and was able to display the wind speed + direction (in near real time) based on ground speed and Airspeed + Heading.
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Old 02-29-2008, 11:06 AM   #6 (permalink)
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Quote:
Originally Posted by dremd View Post
... relied upon the tower to give a radar ground speed and heading, we then (re-)calculated out flight plan based on the wind speed/ direction.
I think that's what he meant. It's analog, but it's still an interface
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Old 02-29-2008, 11:26 AM   #7 (permalink)
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Old 03-10-2008, 06:44 PM   #8 (permalink)
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optiwatch' aero calc

Quote:
Originally Posted by optiwatch View Post
Understanding that HP to overcome aero/drag is helpful. I want to include vehicle weight in my calculations to fully understand the impact of weight.

I came across this, but didn't get to an understandable value. I may just be overlooking some error in my calculations.
Pmotive=1/2*Cd*A*rho*v^3+Crr1*m*g*v
from http://www.geocities.com/greglocock/

My attempt at this calculation is attached on the second tab. Please let me know if anyone can fix it or provide the conversion from Pmotive to HP (or if you have a better spreadsheet). The first tab has the calculation from this discussion (The results look correct to me).

With significant investment, I think I can lower my weight by 200 lbs. Hopefully I can get some idea of the pay back. Spending most of my time at a stead speed (70 mph), I expect less pay back than the average vehicle. Taming my driving habits has already given me a 10% improvement (from average of 27 mpg to a max of 31.5).

I also want to find [easy] ways of reducing my RPMs at highway speeds from current 2750 to about 2200, but that's a different topic...

Thanks.
optiwatch,sorry! I'm way late to the party.I ran your numbers for 70 mph and got 19.1 horsepower aero load at that velocity.I used 0.00238 slugs/ft cubed for density,102.67 feet per second velocity,Cd 0.32,and 25.5 ft-square for frontal area.Sorry,as yet,don't have my estimation stuff for rolling resistance with me.I don't know if your formula also simultaneously figures rolling resistance horsepower.I stuck with what I'm familiar with.Also ,apologize to members for the US Standard notation.I'll put some conversion stuff together and try and post metric units in future.Its tough living in the stone age!
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Old 03-10-2008, 10:38 PM   #9 (permalink)
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Quote:
Originally Posted by aerohead View Post
optiwatch,sorry! I'm way late to the party.I ran your numbers for 70 mph and got 19.1 horsepower aero load at that velocity.I used 0.00238 slugs/ft cubed for density,102.67 feet per second velocity,Cd 0.32,and 25.5 ft-square for frontal area.Sorry,as yet,don't have my estimation stuff for rolling resistance with me.I don't know if your formula also simultaneously figures rolling resistance horsepower.I stuck with what I'm familiar with.Also ,apologize to members for the US Standard notation.I'll put some conversion stuff together and try and post metric units in future.Its tough living in the stone age!
Those numbers sound reasonable. I used the spreadsheet and tried to stick with metric and I got 3.4 kw @ 35 mph and 10.3 kW @ 100 mph, which translates to 4.5 and 13.8 hp. Maybe I got some conversions wrong though.

slugs! *groans*

I always thought it was v^2 not v^3, just from what I remember from my fluid mechanics class.
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Old 03-10-2008, 11:09 PM   #10 (permalink)
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Quote:
Originally Posted by boxchain View Post

I always thought it was v^2 not v^3, just from what I remember from my fluid mechanics class.
v^2 for force... Power is Force*Distance - which is where the extra v for v^3 comes from

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