Unreasonable values for engine torque in vehicle simulation

[rrowe]

TL;DR Summary

While trying to simulate the physics of a Toyota Camry, my values for torque during acceleration seem to be nigh impossible when compared to the car's specified maximum torque.

I'm trying to simulate the physics of a Toyota Camry during acceleration with a time granularity of 100ms. My simulated conditions are as follows:

m = 1590 kg
v = 17 m/s
a = 1.5 m/s²
η (transmission efficiency) = 0.85
r_wheel = 0.35 m
F_drag = 100 N
F_friction = 260 N
F_accel = 1590 kg × 1.5 m/s² = 2400 N
F_total = 100 N + 260 N + 2400 N = 2760 N

The car is in 4th gear with a ratio of 1.46 and a total differential gear ratio of 2.8. This yields a combined effective gear ratio G = 1.46 × 2.8 = 4.088.

I've been operating under the assumption of perfect road traction, yielding the equation:

ω_engine = Gω_wheel

I've been using many of the equations from the Engineering Toolbox. Specifically, here I'm using equation (3) from Car - Required Power and Torque. Rewritten using my naming conventions and solving for torque:

τ_engine = F_tr_wω_w/ω_eη

Given the relationship between angular velocity above, I know ω_w/ω_e = 1/G. This then yields:

τ_e = F_tr_w/Gη

When I solve for torque given the conditions stated, I get:

τ_e = 2760 N × 0.35 m / (4.088 × 0.85) = 278 N⋅m

The specifications list the maximum torque output of the Camry as 184 lb ft ≈ 250 N⋅m. How is it possible that I'm exceeding the maximum torque for this vehicle while accelerating at such a relatively leisurely rate?

 

[jrmichler]

My calculations match yours, so the problem is in the assumptions. Your assumptions include:

Mass
Acceleration
Drag force
Rolling friction force
Wheel diameter
Transmission efficiency
Gear and differential ratios

You can reduce the calculated engine torque from 278 N-m to 250 N-m by some combination of less mass, reduced acceleration, reduced drag force, reduced rolling friction force, smaller wheel diameter, higher transmission efficiency, or lower (larger number) gear and/or differential ratios. Where did the 1.5 $m/s^2$ acceleration come from? Is that supposed to be a real number, or is it assumed for this problem?

 

[rrowe]

Mass was determined from the curb weight of the Camry plus about 100 kg for the driver and fuel. The wheel radius is from the specification for the stock tires, as well as the gear and differential ratios. Drag force was determined using equation (1) from this page and an experimentally determined drag coefficient via wind tunnel test. Friction force was determined using equation (3) from this page.

Note that the page linked in the original post mention in an example:

... The required engine power for a car driving on a flat surface with constant speed 90 km/h with an aerodynamic resistance force 250 N and rolling resistance force 400 N and overall efficiency 0.85 - can be calculated as ...

Those values are relatively close to my computed values, give or take some for the speed difference, difference in drag coefficient, etc.

1.5 m/s² is a chosen number. It was chosen based on research of typical longitudinal acceleration during driving. I also corroborated this by observing similar values with accelerometer readings during a test drive. Anecdotally, this is equivalent to ~3 mph/sec which is a rate I would absolutely expect to see during normal driving conditions.

Is it possible my understanding of automotive powertrains is flawed and there's additional factors altering torque other than the two gear ratios I currently account for?

 

[jrmichler]

Is it possible my understanding of automotive powertrains is flawed and there's additional factors altering torque other than the two gear ratios I currently account for?

Unlikely. The difference between actual and calculated torque is only 10%, and some of your numbers are estimated rather than measured. Some things to check:

1) Check RPM vs road speed to make sure you have the correct tire diameter, transmission gear ratio, and differential gear ratio. Calibrate your speedometer first.

2) Measure your actual aerodynamic drag and rolling friction by a coastdown test. Here's how I tested my truck: https://ecomodder.com/forum/showthread.php/coastdown-test-06-gmc-canyon-20405.html. Note that different tires have different rolling resistance, tire pressure affects rolling resistance, and ambient temperature affects both drag and rolling resistance.

3) Measure the actual acceleration using the same procedure as for the coastdown test. Measuring speed vs time is typically more accurate than an accelerometer.

 

[pbuk]

a = 1.5 m/s² ... v = 17 m/s ... The car is in 4th gear with a ratio of 1.46 ...

How is it possible that I'm exceeding the maximum torque for this vehicle while accelerating at such a relatively leisurely rate?

Leisurely is what you are going to get trying to pull from 40mph in 4th - that's what the gear lever is for