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MAIN HOME PAGE > Technical Info TOC > Mathematical Formulas
  1. Horsepower/torque equation
  2. Liter-to-cubic inch conversion
  3. Carburetor Needs
  4. MPH to RPM Relationships
  5. Finding MPH
  6. Finding RPM
  7. Finding Gear Ratio
  8. Finding Tire Radius
  9. Horsepower to Torque
  10. Cubic Inch Displacement/Volumetric Efficiency


Horsepower/Torque Equation:

Bhp = T × RPM/k

           Where Bhp is Brake Horsepower
                   T is Torque in foot/pounds
                 RPM is engine speed in rounds per minute
                   K is a constant




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Liter to Cubic Inch Conversion


1 Liter = 61.002 c.i.

Cubic Inches to Liters:


 1 c.i. = 0.01639 liter



Relationship between Miles per Hour, (MPH) and Revolutions per Minute, (RPM)

Finding it

First find the vehicle speed, MPH and the consequent engine RPM operating range:

Finding MPH

1) MPH = TIRE RADIUS ÷ 168 × ENGINE RPM ÷ GEAR RATIO
Note: Tire Radius is distance, in inches, from center of tire to ground.
Note: Gear ratio is rear axle ratio multiplied by transmission gear ratio.

Example:
What is the MPH at 6,500 RPM with a 4.90 rear axle and a 14 inch radius tire in 4th gear, (1:1)?

                           14.0 
                  ÷       168.0 
                  ×     6,500.0 
                  ÷         4.90 
                  ÷         1.0
                 _________________
                          111 MPH

Example:
What is the MPH at 6500 RPM with a 4.90 rear axle and a 14 inch radius tire in 3rd gear, (1.34:1)?

                           14.0 
                  ÷       168.0 
                  ×     6,500.0 
                  ÷         4.90 
                  ÷         1.34 
                 _________________
                           83 MPH

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Finding RPM

2

    RPM = 
                             168 
                  ×   Gear Ratio 
                  ×          MPH 
                  ÷  Tire Radius

Example:
Using the above example, what would the RPM be after shifting from 3rd to 4th gear at 83 MPH?

         
                       168.0 
                  ×      4.90 
                  ×     83.0 
                  ÷     14.0 
                 ______________
                     4,880 RPM

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Finding Gear Ratio

  Gear Ratio = 
                      Tire Radius 
                  ×           RPM 
                  ÷           168 
                  ÷           MPH 

Example:
Again, using the above example, what gear ratio is required for 120 MPH at 6,500 RPM?

    
   Gear Ratio = 
                         14.0
                   ×  6,500.0
                   ÷    168.0
                   ÷    120.0
                  ____________
                          4.51

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Finding Tire Radius

4) Tire Radius = 168 × MPH × Gear Ratio ÷ RPM

Example:
Once again using the above example, what is the tire radius for 110 MPH at 6,500 RPM with a 4.11 gear?

   
                        168.0
                  ×     110.0   (MPH)
                  ×       4.11  (Gear Ratio)
                  ÷   6,500.0   (RPM)
                 ___________________________
                         11.685 (11.7)inches

Note: This would be approximately a 23" diameter tire. Speed should also be taken into account since radius will change somewhat due to centrifugal force. The faster the speed, the larger the tire's diameter will be.

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WHAT HP & TORQUE is needed.
Three mathematical formulas are given below in determining horsepower needs:

Engine horsepower required to reach MPH in quarter mile (HPq):

   HPq = 
                      (0.00426 × MPH) 
                  ×   (0.00426 × MPH) 
                  ×   (0.00426 × MPH) 
                  ×            WEIGHT

Note: understates HP required at speeds exceeding 100 MPH.
Note: assumes engine HP must be 2 × the HP required at drive wheels.

Example:
What engine HP is required to achieve 110 MPH in a 3,200 pound vehicle in a 1/4 mile?

HPq = 
                      (0.00426 × 110) 
                 ×    (0.00426 × 110) 
                 ×    (0.00426 × 110) 
                 ×             3,200
                _____________________________
                                 329 engineHP

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Engine horsepower required to sustain MPH on level ground (HPs):

   HPs = 
                                     (MPH ÷  3) 
                +   (WEIGHT ÷ 1,000 × MPH ÷ 10)

Note: assumes engine HP must be 2 × the HP required at drive wheels.

Example:
What engine HP is required to sustain 75 MPH in a 3,600 pound vehicle?

 
    HPs = 
                                       75 
               ÷                        3 
               + (3,600 ÷ 1,000 × 75 ÷ 10)
              _____________________________
                                       25 
               + (3.6 × 7.5)
              _______________________________________
                                        52 engine HP

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Engine horsepower required to sustain MPH up a grade of G% (HPg):

HPg = 
                                              HPs 
               +  (G ÷ 100 × 0.005 × WEIGHT × MPH)

Note: Assumes engine HP must be 2 × HP required at drive wheels,

Example:
What HP to sustain 75 MPH up a 6 % grade in a 3,600 pound vehicle?

HPg =
                          HPs 
               + (6 ÷ 100 × 0.005  x3600 × 75)
              _________________________________ 
                                          HPs 
               +                           81 
              _________________________________
                       (3,600 ÷ 10,000 + 0.33) 
               ×                           75 
               +                           81 
              _________________________________
                                           52 
               +                           81
              _________________________________________
                                          133 engine HP

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a) Horsepower = 
                       TORQUE 
               ×          RPM 
               ÷        5,252 

    Torque =  
                           HP 
               ×        5,252 
               ÷          RPM 

Back to the basics statement:
Horsepower comes from torque.
Torque comes from the pressure of combustion in the cylinder when combustion pressure causes the piston to turn the crankshaft which is measured as torque. The trick is to generate high enough pressure on each stroke and to do it often enough (RPM) to produce the horsepower needed.
Torque is measured in Foot/Pounds.
Foot/Pounds meaning the force of 1 pound exerted on a lever 1 foot in length as measuered from a pivot point.

Example:
What torque is required to generate 329 HP at 6,000 RPM?

  Torque (T) = 
                    329.0
               ×  5,252.0
               ÷  6,000.0
              ______________________
                    288.0  foot pounds @ 6,000 RPM

Example:
What torque is required for 296 HP at 4880 RPM?

  
     T = 
                      296.0
               ×    5,252.0
               ÷    4,880.0 
              ____________
                      319.0  Foot/Pounds @ 4,880 RPM

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About Cubic Inch Displacement, Volumetric Efficiency, Combustion Efficiency and CFM:

1) CID = NUMBER OF CYLINDERS × SWEPT VOLUME

   CID= 
                             N 
                ×            0.7854 
                ×         bore 
                ×         bore 
                ×       stroke (all in inches) 

Example:
What is CID of a V8 with a "30 over", 4 inch bore and 3.48 inch stroke?

 
CID = 
                    8.0 
               ×    0.7854 
               ×    4.030  
               ×    4.030 
               ×    3.48
              _________________________________
                  355.0 Cubic Inch Displacement

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VOLUMETRIC EFFICIENCY (VE)= 

                  Engine Actual Air Intake 
               ÷                       CID:


If VE is less than 1 (or 100%) the amount and quality of charge in the cylinder is reduced so less torque is produced.
Note: VE above 100% is a supercharging effect and more torque is produced.

11) CE = COMBUSTION EFFICIENCY = How well the energy in the fuel is converted into crankshaft torque. Affected by:
air/fuel ratio, ignition timing, charge mixing and other factors.

    Condition       Best Power     Best Economy     Lean Misfire

  Air/Fuel Ratio      12-12.5        14.5-15.5           17

3) CFM = CUBIC FEET PER MINUTE
A measure of air flow into and out of an engine

      CFM = 
                    CID 
               ×    RPM 
               ×     VE 
               ÷   3464 
              __________
               Cubic Feet p/min

Example:
What CFM is consumed by a 355 CID engine at 4,478 RPM if VE = 105%, (1.05)?

 
                   355.0   (CID)
              ×  4,478.0   (RPM)
              ×      1.05  (% VE)
              ÷  3,464.0 
             ______________
                   482.0    CFM

Example:
What CFM by the same engine at 6,400 RPM if VE has fallen to 95% (0.95)?

 
                   355.0   (CID)
              ×  6,400.0   (RPM)
              ×      0.95  (% VE)
              ÷  3,464.0
             _____________
                   623.0    CFM

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About Compression Ratio, Cubic Inches and Horsepower:

4) CR = COMPRESSION RATIO = CYL. VOLUME @ BDC ÷ CYLINDER VOLUME @ TDC

     = 1 + (SWEPT VOLUME ÷ VOL @ TDC) 
     = 1 + (0.7854 × BORE × BORE × STROKE) ÷ (CCV + HGV + PDV) 
     Combustion Chamber Volume (CCV) in cubic inches 

Note: if volume is given in cc’s then divide by 16.4 to get cubic inches.

Head Gasket Volume (HGV) in cubic inches = 
                  Head gasket compressed 
             ×    thickness 
             ×    0.7854 
             ×    bore 
             ×    bore 

                  Piston Deck Volume (PDV) 
             +   Piston Dome Effective Volume
            ___________________________________ 
                 (0.7854 × bore × bore × deck to piston distance) 
             +   (volume of piston depressions - volume of piston bumps) 

Example:
What is CR of the engine if heads have 72 cc chamber, head gasket is compressed to 0.040 inch and flat top pistons give 0.025 deck clearance at TDC?

   CCV = 
                       72.0 
               ÷       16.4 
               __________________________
                        4.39 cubic inches 

   HGV = 
                        0.040 
              ×         0.7854  
              ×         4.030 
              ×         4.030 
             ___________________
                        0.51 CID 
   
   PDV = 
                        0.025 
              ×         0.7854 
              ×         4.030 
              ×         4.030
              +         0.0
              -         0.0 
             ___________________
                        0.32 CID
 
   CR = 
                        1
              + (0.7854 × 4.030 × 4.030 × 3.48) 
              ÷ (4.39 + 0.51+ 0.32) 
             __________________________________
                         1
              + (44.39 ÷ 5.22) 
             __________________________________
                         9.5 Compression Ratio

   HP = 
                 Atmospheric Pressure
              ×                    CR 
              ×                    VE 
              ×                   CID 
              ×                   RPM 
              ÷               5,252.0 
              ÷                 150.8 

Example #1:
What HP from a 350 CID Torker-level engine @ 6,000 RPM at sea level?

 
                        14.7 
              ×          9.5  
              ×          0.95  
              ×        350.0 
              ×      6,000.0 
              ÷      5,252.0 
              ÷        150.8 
             _________________
                       352 HP

Note: Torker VE is typically 100% at Torque peak RPM but 95% at HP peak RPM.

Example #2:
Effect of a carburetor restrictor plate that causes 1.5 PSI additional manifold vacuum?

 
                       14.7 
              ×         9.5 
              ×         0.9 
              ×       350.0 
              ×     6,000.0 
              ÷     5,252.0 
              ÷       150.8 
             _______________
                      336 HP

    CID = 
                            HP 
              ×          5,252.0
              ×            150.8 
              ÷   Atmos. Press. 
              ÷             CR 
              ÷             VE 
              ÷            RPM 

Example #3:
What CID is required for 352 HP from a Performer-level engine?

                   352.0
              ×  5,252.0 
              ×    150.8 
              ÷     14.7 
              ÷      8.5 
              ÷      0.85 
              ÷  5,000.0
             _____________
                   525.0  CID


Note: Performer is 8.5 CR & HP peak is 5,000 RPM @ 85% VE

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