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  Why simulate the performance of competition vehicles?

Simulation allows many different modifications and combinations of modifications to be trialled without building or making any changes to the actual vehicle.  This allows the most performance enhancing solution to be determined without any cost or lost time.

Simulation also allows us to verify that a modification is working correctly, or that the driver is obtaining the most from the vehicle, and can therefore be used as a driver training aid.

Virtual Stopwatch is Competition Car Engineering's own vehicle simulation software.  For further information on how Virtual Stopwatch works read the sections below.

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How does Virtual Stopwatch calculate straight line performance?

Virtual Stopwatch works by using stored/calculated data about the vehicle based on the options you select, including:-

  • An empirical tyre model
  • An empirical suspension model
  • Engine output curves
  • Gear/final drive Ratios
  • Vehicle and driver/passenger mass
  • Wheelbase
  • Track width
  • Centre of Gravity Position
  • Centre of Aerodynamic Pressure
  • Rolling Resistance
  • Transmission losses
  • Clutch engagement/slip model
  • Aerodynamic Resistance
  • Aerodynamic Lift/Downforce
  • Rotating inertia of wheels/tyres/brakes and engine/transmission components
  • Road/Track topography

These factors are used to according to the following process to determine the straight line acceleration:-

  1. First choose the starting road speed.
  2. Determine the engine's speed, RPM, in each gear for the road speed in step 1 using the gear ratio, final drive ratio and the rolling radius of the driven wheels.
  3. Using a look-up table of the engine's power output curve and the RPM's calculated above, determine the engine's power output in each gear, choose the gear with the highest available power.
  4. Multiply the flywheel power by the transmission efficiency to determine the motive power available at the tyre contact patches. Note, Virtual Stopwatch adds an additional calculation to take into account the effect of the driver’s ability to slip the clutch. This only applies below 30mph.
  5. Determine the maximum motive power that can be transmitted by the front and rear wheels (separately) using static mass distribution, downforce/lift generation, and the maximum load transfer due to CG height, wheelbase length, mass and tyre grip coefficient. Since the tyre’s grip coefficient is dependant on the vertical load placed on it this step is iterated several times to determine a final figure. Apply a “grip factor” to the result of the above based on the road bumpiness and the suspension’s compliancy and damping.

  1. Find the maximum accelerative power that can be transmitted by the car, based on step 5, where:- Rear wheel drive = Rear grip only, Front wheel drive = Front grip only, 4 wheel drive = Front and rear grip.
  2. Find the actual maximum motive power which is the lower value of step 4 or step 6.
  3. Determine the power absorbed by resistive forces, where Total resistance = Air drag + Rolling resistance + Gradient “resistance”

The results of steps 3, 6 and 8 can be represented graphically as shown below

  1. Determine the power available for accelerating the car by taking the value from step 7 and subtracting the power absorbed in step 8.
  2. Convert the power remaining to a force using Force = Power / velocity.
  3. Determine the acceleration at the chosen road speed by applying the equation F=mA, where m includes the car’s mass and an allowance for the inertia of the car’s rotating parts.
  4. Determine the time taken to accelerate 1 mph using the result of step 11. If there has been a gear change between the last mph and this one, add in the time required to change gear.
  5. Determine the distance covered whilst accelerating the 1 mph based on the average speed and the time calculated in step 12.
  6. Repeat the above steps for the next mph, until either the car reaches the desired speed (in the case of say 0-62mph), or when a specified distance is covered (for example in the case of 1/4 mile calculation)..

You can see from the explanation above that it is not necessary to use the engine's torque curve to calculate a car's acceleration, see the Power vs Torque explanation page to understand more.

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  How does Virtual Stopwatch calculate cornering performance?

At the heart of the Virtual Stopwatch cornering calculation is a lot of real life data obtained from a range of different cars by the author using Racelogic data acquisition equipment. This ensures the results are very accurate.

The general process by which the cornering performance is calculated is as follows:

  1. Make an initial estimate of the cornering speed (it will be refined later).
  2. Split the car into front and rear ends.
  3. Determine the static forces on the tyre contact patches due to mass distribution
  4. Add/subtract the forces due to aerodynamic lift or downforce.
  5. Add/subtract the forces due to lateral load transfer, multiplied by a factor corresponding to front and rear roll stiffness distribution.


  1. Once the vertical loads on the tyre contact patches are arrived at using the above steps the lateral cornering forces are generated by applying the following equation:- ((A.x^2)+(B.x)+C)*((D.w^2)+(E.w)+F)*G


  • x is the vertical load on the tyre.
  • A, B and C are unique factors for each chassis, derived from on-track data
  • w is the tyre width
  • D, E and F are unique factors for each tyre compound, derived from on-track data
  • G is a factor relating to the tarmac surface.
  1. Use the cornering forces calculated in step 6 to determine the maximum possible cornering G force for each end of the car and select the lowest of the two values.
  2. Multiply this G-force by a factor related to the driver's ability to drive at the grip limit.
  3. Use this amended G-force limit and the corner's radius to determine the car's instantaneous cornering speed.
  4. Repeat steps 4 to 9 for the car's new cornering speed several times until the result is stable.

It should be clear from the process described above that Virtual Stopwatch cannot determine the effect of small suspension changes to a car's performance.  However, since the lateral cornering force calculation factors (described in step 6, above) are derived from real on-track data the process employed has proved to be very accurate, and results can be calculated extremely fast.  In fact after testing many cars it was found that the factors A, B and C were very similar for cars of a similar type if the car was engineered well and set-up properly.

This has allowed the author to accurately predict the cornering performance of cars that have not been track tested by applying the values for these factors from a similar car.  Of course, if the car was not engineered well (lack of chassis torsional stiffness, or insufficient camber recovery in roll, for example) or not set-up properly (non-optimised corner-weights or camber incorrectly set, for example) the new car will fall short of the performance predicted by Virtual Stopwatch.    

To help with optimising Corner-weights you can download Competition-Car-Engineering's corner-weight setting App, here.

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  How does Virtual Stopwatch calculate braking performance?

Description coming soon!

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  How does Virtual Stopwatch calculate Lap times?

First a detailed set of data for each track is needed.  This is obtained by driving the course along the racing line and recording the information required using a datalogger.  Competition Car Engineering uses Racelogic data acquisition equipment.  It is preferable to drive the lap as fast as possible in a vehicle for which a mature mathematical model is already available as this allows the accuracy of the lap time simulation to be thoroughly checked.

The main data required for each track are:-

  • Track Curvature data
  • Track Topography
  • Track Camber

The graphs below show some of the data recorded by the author using a Radical SR3 around the Brands Hatch Grand Prix circuit.

Virtual Stopwatch uses the curvature data to split the track into straights and corners, allowing the processes described in the sections above to be used to calculate the time taken to complete each section of track. 

First the cornering performances are calculated.  This allows the start and finish speeds for each straight to be determined for use in the acceleration/braking calculations.

The time taken to complete the various sections of the track are added together to determine the total lap time.

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  How accurate is Virtual Stopwatch?

The fact that Virtual Stopwatch recalculates the acceleration for every 1mph gain or loss of speed means it has the potential to be very accurate, however the accuracy of any simulation is wholly dependant on the accuracy of the data on which that simulation is based. With good quality data the simulation can be very accurate, as the example below shows of a simulated vs. actual standing-start acceleration run for my own track car.

Virtual Stopwatch uses an extensive vehicle/engine/transmission/tyre database to ensure that the accuracy is as high as possible, as explained below: 

Each engine has its own power curve, rev limit, rotating inertia, and mass.

Each chassis used in the App has its own mass, empirical suspension model and in addition they feature realistic engine, driver, transmission, gearbox, fuel tank, wheel and aerodynamic appendage positions so that changes to any of these components will automatically affect the centre of gravity position as they would in real life.

Each gearbox featured is based on a real gearbox and has the actual gear ratios used in that gearbox.  In addition sequential gearboxes will change gear faster than an H-pattern box.

Different wheel sizes and constructions have different masses and inertias.

Tyre and circuit data has been derived from many hours of testing a wide range of cars on the race-track by the author using Racelogic data acquisition equipment

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COPYRIGHT 2011 Richard Machin. All Rights Reserved