Where do the numbers come from?

Back in 2010, I decided to build a program to determine just how fast cars could go. Now, nearly five years later, the project is in its final stages of completion. The simulator I built in Excel goes through a number of different steps: 

(1) Determining an approximate model for engine torque (and power) by fitting a piecewise polynomial spline curve through known points (i.e. maximum power at such-and-such rpm, etc.) along the speed-versus-force curve in each gear (also correcting the speed for centrifugal expansion of the tire), then correcting it for conditions 

(2) estimating (through published literature on the topic) the efficiency of every component in the driveline (gear meshes, final drive meshes, bearings, oil churning and windage, alternator, rolling resistance, etc.) and applying the power losses to the engine power model (in polynomial form of course) 

(3) finding the total inertia of the car (mass plus the 'effective mass' of the rotating components) and using this to determine the maximum potential acceleration versus speed.

(4) using data about weight distribution, wheelbase length, tire coefficient of friction (tire model is approximated with coulomb friction) and approximate center of mass height to determine the maximum forward acceleration a car can sustain. This will also depend on tire selection; to do this, literature on tire performance in acceleration (under loads similar to real-life conditions) was consulted and a database of tires was created within the simulator's worksheet.

(5) Determining the speed loss from gear changes at a range of speeds near the redline in each gear, and using the calculations to come up with a rough loss percentage. Done by applying an FBD, Newton's second law, and a differential equation, and reading up on advertised shift times (for example, the Ferrari Enzo is often quoted as shifting in 150 milliseconds, and a fast manual shift is often quoted as about 400 milliseconds).

Aerodynamic drag is also estimated with the drag equation, using data determined experimentally from magazine tests.

(6) Using the completed acceleration-versus-speed model to work out the appropriate shift points (if any); this was done by finding out where the acceleration-versus-speed models in each gear intersected with each other (accounting for the percentage speed loss from the shift).

(7) Using all of the above (plus a lot of research into each car's specifications) to work out the numbers. To find time elapsed versus speed, for example, I would apply Newton's Second Law; a rational function with a simple 1 as the numerator, and the car's entire acceleration-versus-speed model (containing a huge number of piecewise parts) as the denominator would need to be integrated (piece-by-piece, along the range each piece applies to) to find the time elapsed from a standstill (or the rollout speed) to the speed for simulation. Also important to note: the fuel economy calculated is done so at the minimum throttle position required to maintain that speed. The difference between the "minimum" and "maximum" are the gears used.

If you have other questions, address me in the comments below.

This simulator is for fun and fun alone. Some of the calculations are pretty accurate, some are not; I used the best performance times I could find in magazine tests (I also accounted for 1-foot rollout in my results) for comparison. I welcome the discussion of my results.

Now, as for other performance benchmarks...

The Ring Tests:
These simulations are designed to calculate the maximum speed which can be attained at high-speed circular test tracks like the Nardó ring in Italy. For these simulations, I used models from published literature (and geometry) to estimate slip angles and increased rolling resistance, them applied them to the acceleration-versus-speed model, set it to zero, and solved for the maximum attainable speed. The tracks used are the Nardó test track in Italy and the Millbrook high-speed bowl in the UK (where the McLaren F1 completed a lap at 195 mph).

Tire critical speed is the speed at which the increased temperature in the tire causes the tire pressure to reach its maximum advertised cold pressure.

The Runway Test
I decided also to do a simulation to compare the maximum speeds attained by different cars on a long runway. The runway used in the simulation is the Bruntingthorpe Aerodrome runway; I used maps of the runway to determine its dimensions (length, maximum radii of the corners at both ends), as well as published or advertised data about each car's maximum cornering and braking abilities to determine the absolute highest possible speeds which can be attained on the nearly two-mile runway.

The Oval Test
I also wanted to know how fast each car could go on the high-speed oval at the Yuma, Arizona Proving Grounds (used by a lot of automotive manufacturers and road testers in the past). The high-speed banking at each corner allows for speeds close to 200 mph at a maximum, and the one-mile straightaways allow for the fastest cars to get very close to their top speeds.

The above picture is the input sheet used in the simulation, where all the data needed to run the simulation of each car goes

Above is the output sheet for the simulation; other calculations (such as gearbox temperatures) are found in other sheets in the file. The whole file is about 2 MB