[DeTomaso] math formula help

Daniel C Jones daniel.c.jones2 at gmail.com
Thu Nov 5 11:20:08 EST 2009


> Math formula wizards---I need your help. What is the RPM on a
> 28'' and 29'' dia tire running at 15 mph 20 mph and 25 mph?

Kirk,

If you mean engine RPM, you need to supply more information,
specifically the gear ratios.  Below are the equations from
a FORTRAN program I wrote that will allow you to compute tire
and engine RPM at a particular speed, given the tire specs or
tire diameter.  Assuming a -2 ZF with 4.22:1 final drive ratio
and 0.705:1 5th gear, you get the following results:

For 28" at 20 MPH:
 Engine RPM = 714.3113942564127
 Tire RPM   = 240.0965998643450
For 28" at 25 MPH:
 Engine RPM = 892.8892428205159
 Tire RPM   = 300.1207498304312
For 29" at 20 MPH
 Engine RPM = 689.6799668682605
 Tire RPM   = 231.8174067655744
For 29" at 25 MPH
 Engine RPM =  862.0999585853257
 Tire RPM   =  289.7717584569681

If you don't write code, you can put the equations into a
spreadsheet like Excel.  As a check case, for a Pantera with
4.22:1 final drive ratio and 0.705:1 5th gear and 335/35/17
tires:

 Vehicle Speed in MPH =   80.00000000000000
 Engine RPM =   3049.789111108714
 Tire RPM =   1025.104739709157
 Overall Gear Ratio (final*transmission) =   2.975100000000000
 Tire Diameter (inches) =   26.23226500000000
 Tire Spec = 335/35/17

If you enter the tire diameter of 26.232265 inches directly,
the program gives the same result.

Dan Jones


      PROGRAM TIRE_RPM

      IMPLICIT NONE
      REAL*8   OPT, WIDTH, AR, WD, MPH, TRPM, ERPM
      REAL*8   GR, FDGR, OGR, K1, K2, PI, TD, TC
      INTEGER  IWIDTH, IAR, IWD

C     Variable Definitions
C     OPT - Input option (1 or 2)
C     TRPM - Tire RPM
C     ERPM - Engine RPM
C     TC - Tire circumference (inches)
C     TD - Tire diameter (inches)
C     MPH - Miles per hour

C     Define constants
C     1 millimeter = 0.039370079 inch)
      K1=0.03937
      K2=12.*5280./60.
      PI=DATAN(1.D0)*4.D0

C     Get user input
 101  CONTINUE
      WRITE(*,*)
      WRITE(*,*)

C     Find engine RPM required at an indicated speed given wheel/tire size and
C     overall drive ratio (gear ratio * final drive ratio).
      WRITE(*,*) 'Enter 1 to compute engine and tire RPM given tire
     . specs'
      WRITE(*,*) 'Enter 2 to compute engine and tire RPM given tire
     . diameter'
      READ(*,*) OPT
      IF (OPT .EQ. 1.0) THEN
        WRITE(*,*) 'Enter tire width in millimeters:'
        READ(*,*) WIDTH
        WRITE(*,*) 'Enter tire aspect ratio (e.g. 60 for 60 series
     . tire):'
        READ(*,*) AR
        WRITE(*,*) 'Enter wheel diameter in inches:'
        READ(*,*) WD
C       Calculate tire diameter
        TD=(K1*WIDTH*AR/100.*2.+WD)
      ELSEIF (OPT .EQ. 2.0) THEN
        WRITE(*,*) 'Enter tire diameter in inches:'
        READ(*,*) TD
      ELSE
        WRITE(*,*) 'Entry error, please try again'
        GOTO 101
      ENDIF

      WRITE(*,*) 'Enter vehicle speed in mph for which engine rpm
     . is desired:'
      READ(*,*) MPH
      WRITE(*,*) 'Enter final drive (rear end) gear ratio:'
      READ(*,*) FDGR
      WRITE(*,*) 'Enter transmission gear ratio:'
      READ(*,*) GR

C     Calculate tire circumference
      TC=TD*PI

C     Calculate tire RPM
      TRPM=K2*MPH/TC

C     Calculate overall gear ratio
      OGR=FDGR*GR

C     Calculate engine RPM
      ERPM=OGR*TRPM

      WRITE(*,*)
      WRITE(*,*) 'Vehicle Speed in MPH =',MPH
      WRITE(*,*) 'Engine RPM =',ERPM
      WRITE(*,*) 'Tire RPM =',TRPM
      WRITE(*,*) 'Overall Gear Ratio (final*transmission) =',OGR
      WRITE(*,*) 'Tire Diameter (inches) =',TD

      IF (OPT .EQ. 1.0) THEN
        IWIDTH=INT(WIDTH)
        IAR=INT(AR)
        IWD=INT(WD)
        WRITE(*,777) IWIDTH,IAR,IWD
      ENDIF

 777  FORMAT(1x,'Tire Spec = ',I3,'/',I2,'/',I2)

 996  FORMAT(A10)

 999  STOP
      END



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