MotorMatchup is the ultimate car specifications website that provides 0-60 times, 1/4 mile times, comparisons and performance simulations. Our goal is to provide high quality automotive data to casual consumers and car enthusiasts alike. When journalists test vehicle performance for 0-60 times and quarter mile times, there are many factors involved (driver, road surface, weather, etc). Simulated performance provides reliable results that consumers can count on without worrying about these external factors. Below we describe in detail the various aspects of how our simulation works. All car data is manually aggregated from manufacturers and various high-quality online resources. If you see any inaccuracies, have questions, or want to get in touch, please don't hesitate to reach out.

## Features

• Compare and drag race up to 3 vehicles side-by-side.
• Simulate 0-60, 1/4 mile, and other performance metrics.
• Add modifications to vehicles and see how performance is affected.
• Extensive specifications including power curves and gearing.

## Limitations

Since public vehicle data can be somewhat limited we may not have all specs for a particular vehicle. For example drag coefficient and transmission shift time are often kept confidential by manufacturers. For unavailable metrics, we estimate them using our parameter prediction software. The methodology for datapoint estimation is explained in detail below.

## Data

Engine
Data PointDescription
HorsepowerPeak horsepower
TorquePeak Torque (ft-lbs)
Peak Power RPMRPM which peak power occurs
Peak Torque RPMRPM which peak torque occurs
Type/ArrangementMotor type and arrangement (e.g "V-8")
Forced InductionDesignates if engine is supercharged or turbocharged
Number of cylindersNumber of cylinders in a piston engine
DisplacementDisplacement of engine (liters)
BoreBore of cyclinder (millimeters)
StrokeStroke of cyclinder (millimeters)
Number of valvesNumber of valves
ValvetrainValvetrain description (e.g "DOHC")
Compression RatioCompression ratio
Battery CapacityBattery capacity in kWh for Hybrids and EVs
Transmission/Drivetrain
Data PointDescription
Transmission TypeType of transmission (e.g "Automatic")
Transmission Sub-typeDetailed type of transmission for automatics (e.g "DCT" or "CVT")
Number of GearsNumber of gears
Gear RatiosList of gear ratios for each gear
Axle ratioFinal Drive/Axle ratio
General
Data PointDescription
Curb WeightVehicle equipped weight w/o occupants (pounds)
Drag CoefficientCoefficient of Drag ($C_d$)
Body DimensionsDimensions of body: length|width|height (inches)
WheelbaseDistance between wheels along length axis (inches)
TrackDistance between wheels along width axis (inches)
Ground clearanceHeight between ground and lowest point on body (inches)
Font Tire SizeFront tire descriptor (e.g "P245/35YR19")
Rear Tire SizeRear tire descriptor (e.g "P305/30YR20")
Tire compoundCategory of tire (e.g "Summer performance")
Fuel Tank CapacityFuel tank capacity (gallons)

## Simulation

The MotorMatchup performance simulation uses data points above to produce a consistent and accurate model. For missing data points, our simulation estimates the value by looking at similar vehicles as well as other factors. This allows the simulation to be robust for a wide variety of cars, even with missing data points. The models have been tested and calibrated against real world results. Below each sub-system is described in detail.

### Torque Curves

#### Internal Combustion Engines

For internal combustion engines, torque curves are derived in 3 steps:
1. Start plotting initial torque curve. The first point is peak horsepower where
$torque = horsepower * 5252 / rpm$
2. Plot 2 more points: torque at idle rpm and torque at peak torque rpm.
3. Use polynomial regression to generate a torque curve function f where
$torque = f(rpm)$
This torque curve function is used for all simulations and it's corresponding horsepower curve can be easily derived from it.

#### Electric Motors

EV drivetrains have more variability. For example number of motors, torque drop off, "redline" RPM, etc. This makes it very difficult to predict torque curves accurately, so our EV torque curves are based on real world dynamometer test data. Because of this, you may notice that some EVs are not supported by the simulation due to unavailable real world data. Note that for futuristic cars where dyno data does not exist yet, some assumptions are made by looking at related vehicle dyno data.

#### Engine Torque vs. Wheel Torque

Whether it's based on real-world dynometer data or estimated, our simulation software defines a torque curve for all vehicles. Torque curves are the foundation of the simulation and used to calculate wheel torque from torque at the motor. In order to convert motor torque to wheel torque, the following equation is used:
$τ_{wheel} = (τ_{motor} * ratio_{gear} * ratio_{axle} * loss_{drivetrain}) / radius_{tire}$

$ratio_{gear}$ - Gear ratio of the current gear.
$ratio_{axle}$ - Final drive or axle ratio.
$loss_{drivetrain}$ - Drivetrain efficiency - (e.g 85% for RWD with Manual Transmission)
$radius_{tire}$ - Dynamic radius of the tire calculated by taking 99% of the resting radius.
Note that this works for vehicles without transmission (e.g Tesla). The gear ratio will be a static value = 1 and drivetrain efficiency ($loss_{drivetrain}$) will be much higher. Also, some cars have variable final drive ratios (e.g Ford Focus RS) which are supported.

#### Drivetrain Loss

Drivetrain loss is variable based on many factors. To keep it simple we use the following drivetrain loss values:
DrivetrainEfficieny
Front-wheel Drive88% (12% loss)
Rear-wheel Drive85% (15% loss)
All-wheel Drive82% (18% loss)
No transmission (EV)95% (5% loss)

### Transmission

#### Shift Time

Shift time is not published by most manufacturers so we estimate this value if it's not known. Here are the parameters we look at:
1. Transmission Type: ("Automatic" or "Manual")
2. Sub-type: ("DCT", "CVT", etc)
3. Holistic parameters (Year, make, and model) which are compared to similar vehicles with known shift times
Shift times for automatic transmissions may be as low as 20ms for a fast dual-clutch transmission like a Porsche PDK and may exceed 500ms for older automatics.The simulation does not support CVT transmissions at the moment as they are difficult to accurately model.Detailed explanations coming soon.

### Aerodynamics

#### Drag Force

Calculated using the formula  $F_d = 0.5 * C_d * A * ρ * {v}^2$
Drag Coefficient ($C_d$) is published for about half of vehicles. For unknown values, $C_d$ is estimated by finding the most similar vehicle with a known drag coefficienct. We use make, model, year, and body style to find the most similar vehicle.
Frontal Area ($A$) is calculated using a simple formula: $A = 0.85 * width * height$

#### Down Force

For most vehicles, downforce is not known so it's not taken into account. However, we do have downforce data for various manufactuers like Koenigsegg. For these few vehicles, it is incorporated into the simulation and will show in higher speed acceleration results.

### Wheels and Tires

Wheels and tires are arguably the most important part in determining a vehicle's performance. There are various components to the model that are described in depth below.

#### Tire Compound

Tire friction is an essential component to car simulations, but it is very difficult to model. In order to support a wide variety of vehicles, we have generalized the tire coefficeint of friction based on tire compound.
Tire CompoundBase Coefficient of Friction
Race Compound1.15
Summer Performance1.075
Performance All-season1.0
All-season0.97
All-terrains0.80

### Conditions

Right now the simulation is based on optimal road conditions. Explanations coming soon.

Q: How do you handle cars that are underrated from the factory?
A: Some cars like Porsche's, McLarens, and BMWs are often underrated from the factory. We manually tag vehicles that have proof of underrating power (Dyno charts from 3rd parties). We are currently working on a more efficient and transparent way to show this information to the user for specific vehicles.

Q: Can you add X or Y car to the website?
A: If the required specifications are available, then yes! Start here.

Q: Does the simulation take into account downforce?
A: For some vehicles, downforce is taken into account. However, for most vehicles it isn't because a lot of that data is not publicly known. We are working on a prediction model for vehicles with unknown downforce data.

### Special Vehicles

The Tesla Roadster is supposed to come out in 2022 or 2023 with over a 600 mile range and a 200kWh battery pack. There have been various rumors and hints of an optional "SpaceX Package" which will add cold-air gas thrusters to the vehicle. The car will have a composite overwrapped pressure vessel (COPV) onboard which will store compressed air. There will be various thrusters mounted around the car and some of those will face backwards. These rear-facing thrusters can be used to add extra thrust and overcome the frictional limits of tires. Our software is able to simulate the added acceleration from these thrusters and this how we calculate it:
$F_{thrust} = (I_{sp})(g)(m_{vehicle})$
where
$I_{sp} = 70s$ (Estimated Specific Impulse)
$g = 9.806 m/s^2$ (Gravitational Constant)
$m_{vehicle}$ (Estimated Vehicle Curb Weight)
The acceleration of the car is then calculated as:
$a_{vehicle} = (F_{thrust} + F_{tire}) / m_{vehicle}$
where
$F_{thrust}$ (Force of Thruster)
$F_{tire}$ (Estimated Tire Force)
The simulation lets you change the curb weight, COPV capacity, max rear-facing thrust, and the firing delay.
Try it out here!