[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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