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Author Topic: Ballast Equations  (Read 17054 times)
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hotrod
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« Reply #15 on: May 02, 2010, 01:58:14 PM »

Here is a basic program I did a few years ago, that has most of that in it.

You can change some of the variables if need be by going into the code.
you will need to have qbasic installed on your system to run these as they run under qbasic.exe in a command window.
I have not gotten around to re-coding this in perl or some other modern language but it works.

===========================
CLS
PRINT
PRINT "              Compute Aerodrag and Rolling drag "
PRINT "        Compute traction available, and max usable power"
PRINT
PRINT


G# = 32.1725
CL# = .2
airden# = .0619
basetiredragcoef# = .0155


REM air density at Bonneville 4214 ft elevetion
REM 90 deg, 30% humidity, barometer 25.7 in Hg abs
REM for denver 5800 ft elevation
REM temp 85, 30% humidity, barometer 23.4 in Hg abs
REM use a value of .056616

REM basetiredragcoef# = .0155
REM suggested value is .011, range from .007 - .013
REM this value (.0155) used based on coast down tests with subaru

INPUT "   Enter frontal area in square ft"; Fa#
PRINT
INPUT "   Enter Cd with decimal "; cd#
PRINT
INPUT "   Enter speed in mph "; mph#
PRINT
INPUT "   Enter weight of car in lbs"; wtlbs#
PRINT
PRINT "   Enter percent weight on drive wheels"
INPUT "   use whole numbers ie 40% = 40 "; drivewt#

REM INPUT "input Coefficient of lift, default is 0.2 if unsure hit enter"; CL#
PRINT
PRINT "   Using coefficient of lift, = "; (INT(CL# * 1000) / 1000)
INPUT "   enter portion of lift applied to drive wheels in percent "; liftdrivewt#
PRINT
INPUT "   Enter Coefficient of friction for the salt conditions ( .4 - .6)"; salttractioncoef#







REM *********************************
CLS
PRINT
PRINT "             Compute Aerodrag and Rolling drag "
PRINT "        Compute traction available, and max usable power"
PRINT
PRINT "     Frontal area = "; (INT(Fa# * 100) / 100); "ft^2    Cd = "; (INT(cd# * 10000) / 10000)
PRINT "     Target speed = "; (INT(mph# * 10) / 10); " MPH"
PRINT "     Car weight   = "; (INT(wtlbs# * 10) / 10); " lbs"
PRINT "     Weight Distribution =  "; (INT(drivewt#)); " %  on drive wheels"
PRINT "     Coefficient of Lift =  "; (INT(CL# * 100) / 100); " ratio of lift to drag"
PRINT "     Lift applied to drive wheels = "; (INT(liftdrivewt# * 1000) / 1000); " Percent"






ftpsec# = mph# * 88 / 60
hpaero# = (((airden# / G#) / 2) * Fa# * cd# * (ftpsec# * ftpsec# * ftpsec#)) / 550

hpaero1# = (((airden#) * Fa# * cd#) / 35389.75) * (ftpsec# * ftpsec# * ftpsec#)
lbaero1# = (((airden#) * Fa# * cd#) / 64.345 * (ftpsec# * ftpsec#))
hprolling# = ((basetiredragcoef# * wtlbs#) + (.00003 * wtlbs# * mph#)) * ftpsec# / 550
lbdragrolling# = ((basetiredragcoef# * wtlbs#) + (.00003 * wtlbs# * mph#))
hptotal# = hpaero# + hprolling#
BHP# = (hptotal# / 84) * 100

REM salttractioncoef# = .4

maxtractionstatic# = ((wtlbs# * drivewt# / 100) * salttractioncoef#)
maxtractionlimitedpower# = (maxtractionstatic# * ftpsec#) / 550
lftlbs# = CL# * lbaero1#
maxtractiondynamic# = maxtractionstatic# - (lftlbs# * liftdrivewt# / 100)
tractionlimitedpower# = maxtractiondynamic# * ftpsec# / 550




PRINT
PRINT "     Using 16% drive train loss"
PRINT "      BHP required at "; mph#; "mph ..................... = "; (INT(BHP# * 1000) / 1000); " HP"
PRINT "      Aero power required is ....................... = "; (INT(hpaero# * 1000) / 1000); " hp "
PRINT "      Rolling resistance is ........................ =  "; (INT(hprolling# * 1000) / 1000); " hp"
PRINT "      Total power at wheels needed at "; mph#; "mph is    = "; (INT(hptotal# * 1000) / 1000); " hp "
PRINT
PRINT "======================="
PRINT "    Aerodrag hp ........................................ = "; (INT(hpaero1# * 1000) / 1000); " HP"
PRINT "    Aerodrag in lbs .................................... = "; (INT(lbaero1# * 1000) / 1000); " lbs"
PRINT "    Estimated lift at 0.2 x drag ....................... = "; ((INT(CL# * lbaero1#) * 1000) / 1000); " lbs"
PRINT "    Percent of lift applied to drive wheels ............ = "; liftdrivewt#; " %"


PRINT
PRINT "======================="
PRINT "    Compute traction available for acceleration"
PRINT "    Assumption Traction Coef on salt "; salttractioncoef#



PRINT
PRINT "======================"

PRINT "    Max tractive thrust which can be delivered (static) ...... = "; ((INT(maxtractionstatic#) * 1000) / 1000); " lbs"
PRINT "    Max usable hp at speed due to traction limitations........ = "; ((INT(maxtractionlimitedpower#) * 1000) / 1000); " HP"

PRINT "    Thrust required to overcome rolling resistance ........... =  "; ((INT(lbdragrolling#) * 1000) / 1000); " lbs"

PRINT "    Portion of lift forces carried by the driving wheels ......=  "; ((INT(lftlbs# * liftdrivewt# / 100) * 1000) / 1000); " lbs"
PRINT
PRINT "    Max thrust lbs deliverable at speed due to lift ...........= "; ((INT(maxtractiondynamic#) * 1000) / 1000); " lbs"
PRINT "    Max useable power at speed due to traction lost to lift ...= "; ((INT(maxtractiondynamic# * ftpsec# / 550) * 1000) / 1000); " HP"
PRINT "    Reserve power available (difference between needed power to reach"
PRINT "    target speed, and power which can be transmitted due to traction limits)"
PRINT
PRINT "******************************************************************"
PRINT "             THESE VALUES MUST BE POSITIVE"
PRINT "                    POWER RESERVE (static).....................=  "; ((INT(tractionlimitedpower# - hptotal#) * 1000) / 1000); " HP"
PRINT "    (how much traction limited power exceeds needed power)"
PRINT
PRINT "    Surplus transferable power at speed (dynamic)..............=  "; ((INT(maxtractionlimitedpower# - hptotal#) * 1000) / 1000); " HP"
PRINT "    Surplus traction thrust after overcoming aero drag ....... = "; ((INT(maxtractiondynamic# - lbaero1#) * 1000) / 1000); " lbs"
PRINT "    Surplus thrust avail for acceleration .................... = "; ((INT(maxtractiondynamic# - lbaero1# - lbdragrolling#) * 1000) / 1000); " lbs"
PRINT "******************************************************************"




======================
copyright Larry Ledwick free to use with attribution.

Noticed a small typo in the code and corrected it for lift applied to drive wheels, was with units of hp, and should have been percent of total lift.

Larry
« Last Edit: May 03, 2010, 08:40:57 AM by hotrod » Logged

interested bystander
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« Reply #16 on: May 02, 2010, 04:43:15 PM »

Isn't there a shortcut formula? Like:

        F=MA, or maybe E=Mc2? (See my Stan Back answer in another post)

Seriously, REALLY extensive , BUT the truth seekers will appreciate.

 Landa's "Automotive Aerodynamics Handbook" has a slew of helpful math similiar to the above (if you can find the book) but not nearly as all-encompassing and Bonnevile specific.

« Last Edit: May 02, 2010, 04:52:30 PM by interested bystander » Logged

5 mph in pit area (clothed)
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« Reply #17 on: May 02, 2010, 06:46:22 PM »

Hotrod...could you compute this for us cd=.3 frontal area 21.5 sq ft.  lift .2  weight 4900 lbs weight on rear wheels 3000lbs  hp 2400
 I didn't see any input for tire width how about the difference between 10'' and 6'' cheers

                 JL222 grin
« Last Edit: May 02, 2010, 06:53:47 PM by jl222 » Logged
hotrod
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« Reply #18 on: May 02, 2010, 10:47:30 PM »

I ran it a couple times and worked the speed up, since you did not mention a target speed.


Looks like you have plenty of power, but need traction (weight on the drive wheels) --- assuming my calculations are correct??

Tire width is largely irrelevant at bonneville as you have very little of the grip you would get with rubber on asphalt where the rubber "gears" itself to the road due to irregularities and glues itself to the road due to adhesion (ie sticky rubber) it is almost all classic sliding friction from what I can tell.

===========================


             Compute Aerodrag and Rolling drag
        Compute traction available, and max usable power

     Frontal area =  21.5 ft^2    Cd =  .2999
     Target speed =  300  MPH
     Car weight   =  4200  lbs
     Weight Distribution =   0  %  on drive wheels
     Coefficient of Lift =   .2  ratio of lift to drag
     Lift applied to drive wheels =  50  lbs

     Using 16% drive train loss
      BHP required at  300 mph ..................... =  1242.067  HP
      Aero power required is ....................... =  961.016  hp
      Rolling resistance is ........................ =   82.319  hp
      Total power at wheels needed at  300 mph is    =  1043.336  hp

=======================
    Aerodrag hp ........................................ =  961.016  HP
    Aerodrag in lbs .................................... =  1201.27  lbs
    Estimated lift at 0.2 x drag ....................... =  240  lbs
    Percent of lift applied to drive wheels ............ =  50  %

=======================
    Compute traction available for acceleration
    Assumption Traction Coef on salt  .5

======================
    Max tractive thrust which can be delivered (static) ...... =  14  lbs
    Max usable hp at speed due to traction limitations........ =  11  HP
    Thrust required to overcome rolling resistance ........... =   102  lbs
    Portion of lift forces carried by the driving wheels ......=   120  lbs

    Max thrust lbs deliverable at speed due to lift ...........= -106  lbs
    Max useable power at speed due to traction lost to lift ...= -85  HP
    Reserve power available (difference between needed power to reach
    target speed, and power which can be transmitted due to traction limits)

******************************************************************
             THESE VALUES MUST BE POSITIVE
                    POWER RESERVE (static).....................=  -1128  HP
    (how much traction limited power exceeds needed power)

    Surplus transferable power at speed (dynamic)..............=  -1032  HP
    Surplus traction thrust after overcoming aero drag ....... = -1307  lbs
    Surplus thrust avail for acceleration .................... = -1410  lbs
******************************************************************


Press any key to continue

==========================


Looks like your top speed should be near 285 mph based on the following.

==========================

             Compute Aerodrag and Rolling drag
        Compute traction available, and max usable power

     Frontal area =  21.5 ft^2    Cd =  .2999
     Target speed =  285  MPH
     Car weight   =  4200  lbs
     Weight Distribution =   71  %  on drive wheels
     Coefficient of Lift =   .2  ratio of lift to drag
     Lift applied to drive wheels =  50  lbs

     Using 16% drive train loss
      BHP required at  285 mph ..................... =  1072.284  HP
      Aero power required is ....................... =  823.951  hp
      Rolling resistance is ........................ =   76.767  hp
      Total power at wheels needed at  285 mph is    =  900.7190000000001  hp

=======================
    Aerodrag hp ........................................ =  823.951  HP
    Aerodrag in lbs .................................... =  1084.146  lbs
    Estimated lift at 0.2 x drag ....................... =  216  lbs
    Percent of lift applied to drive wheels ............ =  50  %

=======================
    Compute traction available for acceleration
    Assumption Traction Coef on salt  .5

======================
    Max tractive thrust which can be delivered (static) ...... =  1491  lbs
    Max usable hp at speed due to traction limitations........ =  1133  HP
    Thrust required to overcome rolling resistance ........... =   101  lbs
    Portion of lift forces carried by the driving wheels ......=   108  lbs

    Max thrust lbs deliverable at speed due to lift ...........=  1382  lbs
    Max useable power at speed due to traction lost to lift ...=  1050  HP
    Reserve power available (difference between needed power to reach
    target speed, and power which can be transmitted due to traction limits)

******************************************************************
             THESE VALUES MUST BE POSITIVE
                    POWER RESERVE (static).....................=   150  HP
    (how much traction limited power exceeds needed power)

    Surplus transferable power at speed (dynamic)..............=   232  HP
    Surplus traction thrust after overcoming aero drag ....... =  298  lbs
    Surplus thrust avail for acceleration .................... =  197  lbs
******************************************************************


Press any key to continue
===========================

This is only theory, it would be good to get some real test cases to compare what it predicts to what people actually experience. To the best of my knowledge it is reasonably correct but limitations to how precise you can know some variables such as percent of lift applied to drive wheels is unknown, I assume 50% on a car but that could be quite wrong on a car which is using a wing for down force.

Larry
« Last Edit: May 02, 2010, 10:55:14 PM by hotrod » Logged

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« Reply #19 on: May 02, 2010, 10:52:28 PM »

what?? more power= more ballast rolleyes
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jl222
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« Reply #20 on: May 03, 2010, 10:07:27 AM »


  Thanks Hotrod ... The 222 car has been timed at 285 mph in the Ist mile at Bville but a blower tubr connector blew off 2 sec or approximately 1100 ft before timing light, computer indicated speed was 312 mph with 1'' of tire growth input.
  Car weighs 4900 not 4200 and there is no tire slip.
  Target speed is as fast as it will go with 2400 hp.

               JL222
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« Reply #21 on: May 03, 2010, 04:18:48 PM »

No matter how you calculate it, what you are doing will help, if and when you run out of horsepower somewhere between the 4 and 5 mile in a roadster you will become a very good driver or be along for the ride. With what it appears you are wanting to do, start with a pretty high gear and work back if needed...

Roadsters just love to dance when they run out of gear or horspower.....Good Luck
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« Reply #22 on: May 03, 2010, 08:16:30 PM »

Sorry about the miscue on the weight -- I was working from home and trying to do that at the same time.

Looks like my numbers agree pretty well with your actual times (given the lack of precision for some of the input values especially).

=========================


             Compute Aerodrag and Rolling drag
        Compute traction available, and max usable power

     Frontal area =  21.5 ft^2    Cd =  .3
     Target speed =  305  MPH
     Car weight   =  4900  lbs
     Weight Distribution =   61  %  on drive wheels
     Coefficient of Lift =   .2  ratio of lift to drag
     Lift applied to drive wheels =  50  percent

     Using 16% drive train loss
      BHP required at  305 mph ..................... =  1319.58  HP
      Aero power required is ....................... =  1010.209  hp
      Rolling resistance is ........................ =   98.238  hp
      Total power at wheels needed at  305 mph is    =  1108.447  hp

=======================
    Aerodrag hp ........................................ =  1010.209  HP
    Aerodrag in lbs .................................... =  1242.06  lbs
    Estimated lift at 0.2 x drag ....................... =  248  lbs
    Percent of lift applied to drive wheels ............ =  50  %

=======================
    Compute traction available for acceleration
    Assumption Traction Coef on salt  .5

======================
    Max tractive thrust which can be delivered (static) ...... =  1494  lbs
    Max usable hp at speed due to traction limitations........ =  1215  HP
    Thrust required to overcome rolling resistance ........... =   120  lbs
    Portion of lift forces carried by the driving wheels ......=   124  lbs

    Max thrust lbs deliverable at speed due to lift ...........=  1370  lbs
    Max useable power at speed due to traction lost to lift ...=  1114  HP
    Reserve power available (difference between needed power to reach
    target speed, and power which can be transmitted due to traction limits)

******************************************************************
             THESE VALUES MUST BE POSITIVE
                    POWER RESERVE (static).....................=   6  HP
    (how much traction limited power exceeds needed power)

    Surplus transferable power at speed (dynamic)..............=   107  HP
    Surplus traction thrust after overcoming aero drag ....... =  128  lbs
    Surplus thrust avail for acceleration .................... =  7  lbs
******************************************************************


Press any key to continue
=========================

Looks like you need to add some weight! ---- see below for additional weight.


             Compute Aerodrag and Rolling drag
        Compute traction available, and max usable power

     Frontal area =  21.5 ft^2    Cd =  .3
     Target speed =  350  MPH
     Car weight   =  5900  lbs
     Weight Distribution =   70  %  on drive wheels
     Coefficient of Lift =   .2  ratio of lift to drag
     Lift applied to drive wheels =  50  percent

     Using 16% drive train loss
      BHP required at  350 mph ..................... =  1987.786  HP
      Aero power required is ....................... =  1526.567  hp
      Rolling resistance is ........................ =   143.173  hp
      Total power at wheels needed at  350 mph is    =  1669.74  hp

=======================
    Aerodrag hp ........................................ =  1526.567  HP
    Aerodrag in lbs .................................... =  1635.608  lbs
    Estimated lift at 0.2 x drag ....................... =  327  lbs
    Percent of lift applied to drive wheels ............ =  50  %

=======================
    Compute traction available for acceleration
    Assumption Traction Coef on salt  .5

======================
    Max tractive thrust which can be delivered (static) ...... =  2065  lbs
    Max usable hp at speed due to traction limitations........ =  1927  HP
    Thrust required to overcome rolling resistance ........... =   153  lbs
    Portion of lift forces carried by the driving wheels ......=   163  lbs

    Max thrust lbs deliverable at speed due to lift ...........=  1901  lbs
    Max useable power at speed due to traction lost to lift ...=  1774  HP
    Reserve power available (difference between needed power to reach
    target speed, and power which can be transmitted due to traction limits)

******************************************************************
             THESE VALUES MUST BE POSITIVE
                    POWER RESERVE (static).....................=   104  HP
    (how much traction limited power exceeds needed power)

    Surplus transferable power at speed (dynamic)..............=   257  HP
    Surplus traction thrust after overcoming aero drag ....... =  265  lbs
    Surplus thrust avail for acceleration .................... =  112  lbs
******************************************************************


Press any key to continue

================



             Compute Aerodrag and Rolling drag
        Compute traction available, and max usable power

     Frontal area =  21.5 ft^2    Cd =  .3
     Target speed =  370  MPH
     Car weight   =  6500  lbs
     Weight Distribution =   70  %  on drive wheels
     Coefficient of Lift =   .2  ratio of lift to drag
     Lift applied to drive wheels =  50  percent

     Using 16% drive train loss
      BHP required at  370 mph ..................... =  2350.117  HP
      Aero power required is ....................... =  1803.503  hp
      Rolling resistance is ........................ =   170.594  hp
      Total power at wheels needed at  370 mph is    =  1974.098  hp

=======================
    Aerodrag hp ........................................ =  1803.503  HP
    Aerodrag in lbs .................................... =  1827.875  lbs
    Estimated lift at 0.2 x drag ....................... =  365  lbs
    Percent of lift applied to drive wheels ............ =  50  %

=======================
    Compute traction available for acceleration
    Assumption Traction Coef on salt  .5

======================
    Max tractive thrust which can be delivered (static) ...... =  2275  lbs
    Max usable hp at speed due to traction limitations........ =  2244  HP
    Thrust required to overcome rolling resistance ........... =   172  lbs
    Portion of lift forces carried by the driving wheels ......=   182  lbs

    Max thrust lbs deliverable at speed due to lift ...........=  2092  lbs
    Max useable power at speed due to traction lost to lift ...=  2064  HP
    Reserve power available (difference between needed power to reach
    target speed, and power which can be transmitted due to traction limits)

******************************************************************
             THESE VALUES MUST BE POSITIVE
                    POWER RESERVE (static).....................=   90  HP
    (how much traction limited power exceeds needed power)

    Surplus transferable power at speed (dynamic)..............=   270  HP
    Surplus traction thrust after overcoming aero drag ....... =  264  lbs
    Surplus thrust avail for acceleration .................... =  91  lbs
******************************************************************


Press any key to continue

========================

As you can see according to these calculations (again just theory) you need 4550 lbs on the rear wheels to use all your power, and given enough acceleration time, you should get close to 370 mph with that much power if you can hang on to it.

Not sure 70% of weight on the rear is safe, but the actual weight on the drive wheels necessary to hook that much power won't change if salt conditions allow .5 coefficient of friction (and all other assumptions are correct like amount of lift etc.

Good luck!
I will try to look you up this year.

Larry

« Last Edit: May 03, 2010, 08:24:16 PM by hotrod » Logged

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« Reply #23 on: May 04, 2010, 12:47:58 PM »


  Yeah Larry look us up Langlo racing on trailer and we like to be on the front row to watch when we can.
  The 285 mph is right on with our timing slip but as noted the car was coasting for 1100 ft or 2 sec + as seen on video
and rpm indicated 312 mph we also had a 268 mph 21/4 speed which shows that the car coasting through the lights had an increase of 17 mph from that average and 44 miles and hour from the 312 mph indicated speed.
  As far as weight on rear wheels we have 3000 lbs static [but] we also have a spoiler which also increases down force, but how much we don't know but as you can see the car hooks extreamely well for conditions.
  Talking to Goodyear guy at 200 mph banquet about there testing on salt coef. [they were surprised when results showed
 .7 shocked] if I remember right he also said the salt seperated from itself before the tires spun.
 The Bonneville Pro computer program shows a top speed of 341 but well have to see what happens in the real world.
  Yeah come by and maybe you can fine tune your program with our results if we can make a full pass.

                     JL222 cheers
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« Reply #24 on: June 18, 2010, 03:08:58 PM »

Here is Larry's routine in xls. Sheets are protected but no password required.  grin

Thanks Larry!!

* LL_Aero_Rolling_Drag.xls (77.5 KB - downloaded 353 times.)
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« Reply #25 on: July 06, 2010, 12:11:35 AM »

Comments on Hotrod’s above calculation sheets:

1)  It may be worth including the front-to-rear weight transfer due to the aero drag acting on a CP above ground level.  For some configurations this would be of minor importance, but for the more upright, short wheelbase, and high horsepower vehicles such as roadsters and motorcycles, it could amount to a significant load redistribution.

2)  The rolling resistance calculation is presented as proportional to velocity.  More details on its origin and applicability would be interesting.  Others, (Korff’s Goldenrod paper), have a quadratic relation in velocity.  This may make more sense since at higher speeds, the tires and wheels are subject to a velocity squared aero drag and turbulence.  Comparing the two, there can be a significant difference at higher speeds.  Of course, it could be argued that the velocity squared component could be absorbed into the vehicle drag coefficient but aerodynamicists would probably prefer not to contaminate the results of their shapes, calculations, and wind tunnel data with what the wheels may be contributing, if that could even be reasonably determined short of being on the salt.

3)  Some of the terminology used does not clearly convey just what the numbers really represent.
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« Reply #26 on: July 06, 2010, 08:31:29 PM »

  how much different  if roadster is front wheel drive  ?
 never thought much about that..............
 6 weeks to go
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« Reply #27 on: July 07, 2010, 08:14:03 PM »

Calculating the drag-related weight transfer is relatively simple if a couple quantities are known or can be estimated.  dW = (D*h)/WB  where dW is the weight transfer (lb), D is the drag force (lb), h is the height of the center of pressure above the ground, and WB is the wheelbase.  h and WB should have the same units, e.g. inches, feet, or whatever. 

By way of illustration, assuming drag of 1600 lbs, h of 20”, and a wheelbase of 80”, the front end will get 400 lbs lighter and the rear 400 lbs heavier.  Perhaps not a big effect, but at least accounting for it would get the traction calculation that much closer to reality.

As regards a front-drive roadster, this weight transfer would eventually limit the speed achieveable since traction required is increasing in order to overcome the increasing drag, but the traction available is decreasing as the drive axle weight is decreasing.  Such a roadster would probably be inherently front-heavy, and the limit may be beyond the power available, but in any case, the remedy is straightforward--ballast up the front or induce some aero downforce.  And, adding ballast to the front is much more friendly to aerodynamic stability than having to add it to the rear.
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« Reply #28 on: July 07, 2010, 09:38:42 PM »

Good points there, I will need to consider putting that in the calculation.

It might be more practical due to all the complicating considerations to do that as a second followup calculation as you did in the preceding post.

The only question I would have is how to properly estimate the center of pressure height.

It might be reasonable to assume the center of pressure is at the center (centroid) of the frontal area.

That would probably be reasonable for a clean well designed body with good aerodynamics like a lakester or stream liner. I suspect that assumption would break down in the case of body styles like the older pickup trucks where the "green house" of the cab might create a larger fraction of the drag compared to the front end, especially on some of the really old body styles which had near flat and near vertical windshields.

A large good scoop elevated well above the hood line could also act like a lever and if it was a high drag scoop might substantially raise the center of pressure.

It certainly is something to think about for people that have high drag and high profile body shapes, like the roadsters, older pickups and diesel trucks.

In the case of front wheel cars it is definitely something to consider as it inherently will reduce traction on the drive wheels.

Larry
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« Reply #29 on: October 16, 2010, 04:58:39 PM »

Sorry about the miscue on the weight -- I was working from home and trying to do that at the same time.

Looks like my numbers agree pretty well with your actual times (given the lack of precision for some of the input values especially).

=========================


             Compute Aerodrag and Rolling drag
        Compute traction available, and max usable power

     Frontal area =  21.5 ft^2    Cd =  .3
     Target speed =  305  MPH
     Car weight   =  4900  lbs
     Weight Distribution =   61  %  on drive wheels
     Coefficient of Lift =   .2  ratio of lift to drag
     Lift applied to drive wheels =  50  percent

     Using 16% drive train loss
      BHP required at  305 mph ..................... =  1319.58  HP
      Aero power required is ....................... =  1010.209  hp
      Rolling resistance is ........................ =   98.238  hp
      Total power at wheels needed at  305 mph is    =  1108.447  hp

=======================
    Aerodrag hp ........................................ =  1010.209  HP
    Aerodrag in lbs .................................... =  1242.06  lbs
    Estimated lift at 0.2 x drag ....................... =  248  lbs
    Percent of lift applied to drive wheels ............ =  50  %

=======================
    Compute traction available for acceleration
    Assumption Traction Coef on salt  .5

======================
    Max tractive thrust which can be delivered (static) ...... =  1494  lbs
    Max usable hp at speed due to traction limitations........ =  1215  HP
    Thrust required to overcome rolling resistance ........... =   120  lbs
    Portion of lift forces carried by the driving wheels ......=   124  lbs

    Max thrust lbs deliverable at speed due to lift ...........=  1370  lbs
    Max useable power at speed due to traction lost to lift ...=  1114  HP
    Reserve power available (difference between needed power to reach
    target speed, and power which can be transmitted due to traction limits)

******************************************************************
             THESE VALUES MUST BE POSITIVE
                    POWER RESERVE (static).....................=   6  HP
    (how much traction limited power exceeds needed power)

    Surplus transferable power at speed (dynamic)..............=   107  HP
    Surplus traction thrust after overcoming aero drag ....... =  128  lbs
    Surplus thrust avail for acceleration .................... =  7  lbs
******************************************************************


Press any key to continue
=========================

Looks like you need to add some weight! ---- see below for additional weight.


             Compute Aerodrag and Rolling drag
        Compute traction available, and max usable power

     Frontal area =  21.5 ft^2    Cd =  .3
     Target speed =  350  MPH
     Car weight   =  5900  lbs
     Weight Distribution =   70  %  on drive wheels
     Coefficient of Lift =   .2  ratio of lift to drag
     Lift applied to drive wheels =  50  percent

     Using 16% drive train loss
      BHP required at  350 mph ..................... =  1987.786  HP
      Aero power required is ....................... =  1526.567  hp
      Rolling resistance is ........................ =   143.173  hp
      Total power at wheels needed at  350 mph is    =  1669.74  hp

=======================
    Aerodrag hp ........................................ =  1526.567  HP
    Aerodrag in lbs .................................... =  1635.608  lbs
    Estimated lift at 0.2 x drag ....................... =  327  lbs
    Percent of lift applied to drive wheels ............ =  50  %

=======================
    Compute traction available for acceleration
    Assumption Traction Coef on salt  .5

======================
    Max tractive thrust which can be delivered (static) ...... =  2065  lbs
    Max usable hp at speed due to traction limitations........ =  1927  HP
    Thrust required to overcome rolling resistance ........... =   153  lbs
    Portion of lift forces carried by the driving wheels ......=   163  lbs

    Max thrust lbs deliverable at speed due to lift ...........=  1901  lbs
    Max useable power at speed due to traction lost to lift ...=  1774  HP
    Reserve power available (difference between needed power to reach
    target speed, and power which can be transmitted due to traction limits)

******************************************************************
             THESE VALUES MUST BE POSITIVE
                    POWER RESERVE (static).....................=   104  HP
    (how much traction limited power exceeds needed power)

    Surplus transferable power at speed (dynamic)..............=   257  HP
    Surplus traction thrust after overcoming aero drag ....... =  265  lbs
    Surplus thrust avail for acceleration .................... =  112  lbs
******************************************************************


Press any key to continue

================



             Compute Aerodrag and Rolling drag
        Compute traction available, and max usable power

     Frontal area =  21.5 ft^2    Cd =  .3
     Target speed =  370  MPH
     Car weight   =  6500  lbs
     Weight Distribution =   70  %  on drive wheels
     Coefficient of Lift =   .2  ratio of lift to drag
     Lift applied to drive wheels =  50  percent

     Using 16% drive train loss
      BHP required at  370 mph ..................... =  2350.117  HP
      Aero power required is ....................... =  1803.503  hp
      Rolling resistance is ........................ =   170.594  hp
      Total power at wheels needed at  370 mph is    =  1974.098  hp

=======================
    Aerodrag hp ........................................ =  1803.503  HP
    Aerodrag in lbs .................................... =  1827.875  lbs
    Estimated lift at 0.2 x drag ....................... =  365  lbs
    Percent of lift applied to drive wheels ............ =  50  %

=======================
    Compute traction available for acceleration
    Assumption Traction Coef on salt  .5

======================
    Max tractive thrust which can be delivered (static) ...... =  2275  lbs
    Max usable hp at speed due to traction limitations........ =  2244  HP
    Thrust required to overcome rolling resistance ........... =   172  lbs
    Portion of lift forces carried by the driving wheels ......=   182  lbs

    Max thrust lbs deliverable at speed due to lift ...........=  2092  lbs
    Max useable power at speed due to traction lost to lift ...=  2064  HP
    Reserve power available (difference between needed power to reach
    target speed, and power which can be transmitted due to traction limits)

******************************************************************
             THESE VALUES MUST BE POSITIVE
                    POWER RESERVE (static).....................=   90  HP
    (how much traction limited power exceeds needed power)

    Surplus transferable power at speed (dynamic)..............=   270  HP
    Surplus traction thrust after overcoming aero drag ....... =  264  lbs
    Surplus thrust avail for acceleration .................... =  91  lbs
******************************************************************


Press any key to continue

========================

As you can see according to these calculations (again just theory) you need 4550 lbs on the rear wheels to use all your power, and given enough acceleration time, you should get close to 370 mph with that much power if you can hang on to it.

Not sure 70% of weight on the rear is safe, but the actual weight on the drive wheels necessary to hook that much power won't change if salt conditions allow .5 coefficient of friction (and all other assumptions are correct like amount of lift etc.

Good luck!
I will try to look you up this year.

Larry


who says hotrodding is'nt rocket science.?
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