Keep in mind that with towing, just because your engine can make 200 ft-lbs of torque doesn't mean it was designed to do it continuously. Your engine and transmission will need to dissipate a lot of heat. Towing your vehicle's max capacity up a mountain at high noon in the middle of summer is a surefire way to blow or crack expensive parts of your drivetrain. Hot engine = hot oil, means you need to check and replace it more frequently if you're towing heavy loads. Also, just because I can put a class III hitch on my crosstrek, and just because the calculations say I can pull 3000 lbs up a steep hill, doesn't mean the body of the car can handle that sort of stress. Use common sense. When pulling uphill, stop when necessary to let things cool down. Also, if my calculations show that I can pull 3000 lbs up a 30% grade at 23 mph, that means I literally cannot go any faster or slower than that, without sliding down the high or low RPM ends of the torque curve. A realistically climbable grade is going to be MUCH LESS than the calculations show, especially if you might need to start from a dead stop (then the limiting factor is your poor, soon to be fried, clutch).
Keep in mind that with braking, things can really heat up. Just because your tires can stop quickly enough, doesn't mean your brakes can dissipate the energy quickly enough. Brake energy dissipation is very complicated, and dependent on ambient air temperature, wheel design (open spoke = better airflow), vehicle speed, wind, etc. Also, under-inflated tires get very, very hot from constant sidewall flex, and coupled with intensive braking, can cause a blowout. When driving downhill for long periods of time, engine braking helps keep your brakes cooler, in case you suddenly need them. It also saves gas in modern cars, which will cut the injectors when the engine is driven by the wheels.
This is a worked example for my vehicle and a proposed trailer weighing 3000 lbs. I will be calculating maximum load capability, and stopping distance.
Here's a list of numerical values you will need:
µs = Coefficient of static friction for tires = 0.7 dry road; 0.4 wet road
M1 = Curb weight of tow vehicle + cargo = 3,109 lbs + 500 lbs = 3609 lbs (1637 kg)
M2 = Mass of trailer = 3000 lbs (1361 kg)
T = peak torque = 145 lb-ft (196 N m)
ω = peak rpm = 4200 rpm (70 s^-1)
G = lowest gear ratio = 4.444 (Drive axle ratio) * 3.545 (transmission) = 15.754
R = driven tire radius = 14.5 inches (36.83 cm)
Ok, got all of that? Great! Let's do some calculations
For determining the maximum grade your vehicle can climb, use the following formulas:
First, determine the amount of force you can provide
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F1 = T * G / R = 196 N m * 15.754 / 36.83 cm = 8384 N
Then, the weight of the vehicle and trailer
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F2 = (M1 + M2) * 9.81 m/s^2 = (1637 kg + 1361 kg) * 9.81 m/s^2 = 29410 N
Finally, we can determine the maximum grade the rig can ascend under optimum conditions
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sin^-1(F1/F2) = sin^-1(8384 N/29410 N) = 16.56 degrees
16.56 degrees is a 30% grade, so that's pretty steep!
You can also determine exactly how fast you need to be going to make it up that hill
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ω / G * 2πR = 70 s^-1 / 15.754 * 2 * 3.142 * 36.83 cm = 23 mph (37 km/h)
More importantly, we need to examine stopping distances:
*Note: Keep in mind, these calculations do not factor in air resistance, or rolling resistance, so actual stopping distances will be a little bit lower than the calculations (stop sooner). However, air resistance accounts for less than 6% of braking force at 70 mph, and drops off exponentially as the vehicle slows down.
Scenario 1: No trailer brakes
First, we need to calculate braking force:
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Fb = (M1 + (M2/10)) * 9.81 m/s^2 * µs = (1637 kg + (1361 kg /10)) * 9.81 m/s^2 * 0.7 = 12176 N
Then, we can relate vehicle velocity (Vi) and stopping distance (D) as follows:
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((M1 + M2) * Vi / Fb) * Vi/2 = D
1/2 * (1637 kg + 1361 kg) / 12176 N * Vi^2 = D
If we plug in 60 mph, we get 290 feet of stopping distance! That's quite normal and acceptable at 60 mph!
Scenario 2: Trailer brakes
This is where things might surprise you a little bit. The stopping distance, with trailer brakes, is identical to the stopping distance of the vehicle, without a trailer attached. This is because, when all wheels have brakes, the frictional force that can be applied is proportional to the total mass, and so is momentum. Therefore, the formula becomes very simple:
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1/2 / (9.81 m/s^2) / 0.7 * (Vi)^2 = D
At 60 mph, this is 172 feet of stopping distance. In fact, all vehicles can stop in 172 feet at 60 mph. The limiting factors are tire integrity and brake fade.
) I leave even more than 3 seconds unless someone's just cut me off. . . Then I slow down to create my gap again.
