HOWTO: Calculate towing speed/grade speed

[Old Blue]

This mini-howto was inspired by the thread 7.3IDI towing limit? and covers how you can accurately estimate how fast your truck can pull a given weight, on the level or up any % grade. I have broken the material down into 4 smaller sections. Many will not have a need for this, but it may be interesting to a few perhaps. Anyone can do these calculations with basic math (Algebra/Pre-Algebra) so nothing too difficult. To calculate this for your truck you will need:

1. Your dyno graph (or one from a similarly equipped truck) must be true rear wheel horsepower
2. Your truck weight and/or combined truck and trailer weight
3. For trailers, the width and height, to make a rough guess of frontal area
4. Gear ratios for your transmission and rear end
5. Road surface types you plan to encounter (concrete, asphalt, etc)

People often wonder how much weight their truck will pull, and what speed they might be able to maintain running up a grade. The good news is, these calculations are available to anyone with some dyno data, truck weight, and a little spare time. Having this information will give you a much better picture of how your truck will tow on the Interstate or even local roads, allowing you to have a much better idea of what speed and gears you will be able to pull on certain hills, for example.

There are three primary factors we need to consider when figuring out how much power a given road speed will require:

1. Wind Resistance (Drag)
2. Rolling Resistance (Friction)
3. Grade Resistance (Inclines, hills)

The next installment will cover wind resistance in detail. Keep in mind, these calculations will tell you how much power you will have for a given load, but does not address suspension, tires, brakes or any other limitations that you will need to address separately.

 

[Old Blue]

Calc 1 of 4: Wind Resistance

Calc 1 of 4: Wind Resistance

You must be registered for see images attach

HP - Horsepower required
Cd - Coefficient of drag
A - Frontal Area in square feet
mph - Road (wind) speed in Miles Per Hour

Equations such as the one above can be supremely helpful, but sometimes getting them in the right form so that you can make use of them can take some work. The formula above has already been tailored for power requirements in horsepower, and requires us to input road speed, Cd and frontal area from the manufacturer, or best guesses.

Example: For most of my guesswork for a pickup truck alone, I have been using 35 sq. ft. and a Cd of 0.50. This gives us the following results:

MPH	HP Required
5	0.01
15	0.4
25	1.83
35	5.03
45	10.68
55	19.51
65	32.2
75	49.46

As you can see, wind resistance really only becomes significant above 35 mph. For the purpose of all future calculations, all wind resistance will be used for is to subtract from our available rear wheel horsepower at a given speed.

When you add a trailer, you will need to modify the frontal area and the Cd to reflect the larger body, if the body extends beyond the frontal profile of the truck. Almost all trailers will require a modification of this figure to reflect the increased drag.

 

[Old Blue]

Calc 2 of 4: Rolling Resistance

Calc 2 of 4: Rolling Resistance

You must be registered for see images attach

Rolling resistance is caused by the tires flexing, bearing drag, and tire sinking into a soft road surface. The two primary factors that determine the rolling resistance are gross vehicle weight and road surface type. We will assume appropriate tires and inflation will be used for whatever surface and GVW you are using here. In heavy truck applications, we can approximate this resistance from a table, based on these two factors.

We will refer to the rolling resistance in lb/ton (pounds per ton) - Later on, we will take our known engine horsepower and gearing, to see how many pounds of force your truck can put to the ground - so these figures will match up later on! The fancy-pants way that lb/ton is referred to in text books is called “tractive effort”.

Rubber Tires, High Inflation Pressure​

Road Surface Type	Rolling Resistance (lb/ton)
Smooth Concrete	35
Good Asphalt	40 - 65
Earth, compact & maintained	40 - 70
Earth, poorly maintained	100-140
Loose sand and gravel	260 - 290

Now we have a chart, but what do we do with it, and what do the numbers mean? What that chart gives you is how much rolling resistance, in pounds, your truck’s engine has to overcome, for each ton of vehicle weight. We take the number for the road surface we’re interested in and multiply it by the actual weight (in tons) of our truck or truck & trailer combo.

Example: You have a car parked in your smooth, level concrete driveway. The car weighs exactly 2 tons, or 4,000 lbs. Using the table above, it would require a constant applied force of 70 lbs. (35 x 2 tons) to overcome the rolling resistance - most adults can apply this amount of force, and move the car by hand.

 

[Old Blue]

Calc 3 of 4: Grade Resistance

Calc 3 of 4: Grade Resistance

You must be registered for see images attach

As you encounter a hill, you know from experience that you have a harder time, and use more power the steeper the grade. You may also have seen grades on Interstates and other roads labeled with a percentage (%). This percentage indicates how many feet the grade rises in a given 100 foot horizontal run.

You must be registered for see images attach

That 5 ft. rise in the example above may not seem like much, but those who have towed before will know that a 5% grade is no joke. Food for thought, imagine how much work it would take you, if you broke your truck into many smaller 100 lb. pieces, and had to lift each one off the ground and put it up on a shelf 5 ft. off the ground. I bet you’d be pretty tired - and that is how much work your engine has to do, in the space of every 100 ft. of road, the whole way up the hill! Now imagine that same exercise, but with a loaded truck and trailer. You better have a lot of power! Unfortunately, your truck cannot eat Wheaties.

Conveniently, the additional force required to pull up a grade uses the SAME units we use for rolling resistance, and ultimately available truck power, later on. There is a generalization, that for every 1% of grade, the effort required to move the truck increases by 20 lb/ton (this works well up to about 10% grade). To make things even simpler, we have another chart!

Grade (%)​	lb/ton​	Grade (%)​	lb/ton​
1​	20​	12​	238.4​
2​	40​	13​	257.8​
3​	60​	14​	277.4​
4​	80​	15​	296.6​
5​	100​	20​	392.3​
6​	119.8​	25​	485.2​
7​	139.8​	30​	574.7​
8​	159.2​	35​	660.6​
9​	179.2​	40​	742.8​
10​	199.0​	45​	820.8​
11​	218.0​	50​	894.4​

Example: Let’s say our truck weighs 3 tons, and we are coming up on a 3% grade. To pull the grade, we will need to apply 60 pounds of power for each ton of the trucks weight, or 180 pounds of total force to move up the hill.

 

[Old Blue]

Calc 4 of 4: Power

Calc 4 of 4: Power

People know what power is when talking about trucks, cars, and anything that burns fuel and moves! It’s that Tim Allen, Home Improvement-ish inspiration that you feel when your head snaps back taking off from a light, or that stump-pulling grunt of a diesel truck. The hard-core can even quote you their peak HP and Torque numbers from the latest dyno or manufacturer spec sheet. But we want to know how much real work can be done, not some arbitrary numbers!

First, let’s try to understand what power is a little bit. Torque is a twisting force - it is the meat and potatoes of real work when we talk about engines. We can get torque in one of two ways - we can generate it directly with the engine, or we can “gear down” - make the output shaft turn slower, but multiply the torque at the wheels by using our transmission’s lower gears. When you gear down like that, you are doing the same amount of work, but giving your engine more mechanical advantage to pull something it couldn’t otherwise pull. This works because we are spreading the heavy workload out over a longer period of time in a lower gear. The faster you climb a hill for example, means you are performing more work faster than if you had to gear down and attack the hill more slowly to reach the top.

That is where the other term for power comes in - horsepower. This is different than torque in that it is not a “force” of any kind (remember how torque is a twisting force). Horsepower refers to how fast you can perform a given amount of work. Any time you talk about how fast you can do something, drive the ¼ mile, reach the top of a 6% grade with a 10k trailer, you ultimately are talking about horsepower. Horsepower ties the torque your engine produces to how fast it can deliver that torque. Horsepower is directly related to RPM’s, because RPM’s are a measure of speed. If an engine can produce 100 ft. lbs. of torque at 1000 RPM and can also produce 100 ft. lbs. of torque at 2000 RPM, then the engine makes twice as much power at 2000 RPM - it can accomplish the same amount of work twice as fast.

In engineering speak, horsepower refers to the rate at which work is done.

1 HP = 33,000 ft. lbs. per minute​

At the end of the day, all the torque and horsepower are doing in your truck is pushing it down the road, in a relatively straight line. The mechanicals (transmission, rear end, and tires) convert your engine’s rotational power into straight line motion, or in the techy jargon “tractive force.” Basically your truck takes all the twisting effort of the spinning engine and “lays” it down on the road, so to speak. Assuming the road is not slippery, we can lay down all of the power that reaches the tires.

Tractive force is really simple - it’s how many pounds you can generate to push your truck forward. Forget engines for a second, and just imagine a “force” like an imaginary tow truck dragging your truck down the road. We could measure that force of being dragged if we put a spring scale between the tow truck and our vehicle - and in turn, measure how much force we have applied for that forward motion.

Now we must convert from our engines dyno HP and TQ numbers into real power numbers that can do meaningful work - putting that power down on the road. The term for this is called “Rimpull.” Rimpull is the usable power at the point of contact between the tire and the ground. It is measured in pounds of pull, just like in our tow truck example. There is a simple equation to figure out Rimpull:

You must be registered for see images attach

Using this equation, it takes into account the speed of your truck. As the speed of your truck goes up, you will have less available rimpull to pull your load. At the point your three resistance factors (wind, rolling, grade) exceed your Rimpull, your will no longer be able to go any faster. If your resistance numbers exceed your Rimpull, your truck will slow down until they at least become equal again.

Example: Your truck generates 120 rwhp (rear wheel horsepower) and you are traveling 65 MPH on a 1% Grade. Your truck and trailer combined weigh 18,000 lbs (9 tons). Your trailer fits fully inside the frontal profile of the truck, so we can use the wind resistance numbers from earlier. The road conditions are smooth concrete. (Click on Images to enlarge as needed)

Step 1 - Subtract the HP used for Wind Resistance from the rear wheel horsepower:

You must be registered for see images attach

Step 2 - Calculate your Rimpull:

You must be registered for see images attach

Step 3 - Calculate Rolling Resistance using the chart in that section:

You must be registered for see images attach

Step 4 - Calculate Grade Resistance using the appropriate chart:

You must be registered for see images attach

Step 5 - Subtract all resistance from your Rimpull number:

You must be registered for see images attach

​

Congratulations! The leftover power (14.24 lbs) is a positive number, which means the truck should (barely) be able to pull the load up that grade at that speed - if the number at the end of your calculation is negative, then the load exceeds the trucks available horsepower, and your truck will not be able to travel at that speed and will slow down.

You’re Not Done!

If only it was that simple - but there is one important piece of the puzzle missing, and that is concerning the Rear Wheel horsepower number. In order to use the Rimpull equation above, we have to know how much actual horsepower the engine can provide at a certain road speed. Because of our fixed gear ratios, and the way engines work, they do not produce peak HP at all RPMs (and road speeds.) To figure out the actual rwhp for a given speed, you need to know how fast your engine is turning at that MPH, and look at the dyno chart to see how much HP the engine develops at that specific RPM. Maybe you’ll get lucky and it happens to be at or near the peak HP that your engine develops - but then again, maybe not! If you have overlapping gear ratios, you can try your calculation at each RPM (and subsequent HP rating) to see if one gear will help you hold a given speed.

If you need help calculating RPM vs true Road Speed (using the tach and your speedometer in your old truck is not likely to yield accurate results), we can cover that if need be, we need gear ratios and tire sizes to make an accurate measurement.

If anyone has some real world examples they want to try, post em up and we’ll see what we get. We need a dyno sheet of your truck or one similarly equipped, the actual weight of your rig, and the road conditions such as % Grade and surface type. If your trailer is larger than your truck, we’ll need to calculate the frontal area and Cd for use in our Wind Resistance numbers.

 

[ChevyTrucks1]

Thanks Old Blue; very helpful.

 

[laserjock]

That was an interesting read.

 

[[email protected]]

Ok so I worked everything out for my setup. Can someone please verify? I have a 2300 pound Chevy Spark and I want to tow a 1400 lb boat plus I weigh close to 200 for math simplicity. So my combined weight is estimated at 3900 lbs. My Chevy Spark has a 1.2L engine (84 HP @ 6400 RPM). Although It makes 84 HP @ 6400 I want to use my HP at 4500 RPM not 6400 RPM. I obviously do not want to tow anything screaming at 6400 RPM up a mountain. So I deleted the 84 HP and replaced it with a figure of 72 HP since that's what the dyno chart on the automobile-catalog website says I make at 4500 RPM. I am wanting to tow this boat from Seattle to Indianapolis so the highest elevation I'm going to encounter is going to be 5,500 feet in Butte, Montana. So using the Wallace Racing elevation calculator I lose 16.5% power at 5500 feet. So my 72 Crank HP at 4500 RPM with elevation loss at max altitude is 72 X .835 =60.12 Crank HP @ 4500 RPM @ 5500 feet elevation. After that I subtracted the standard 15% for your typical power loss going through a modern 5 speed transmission. 60.12 x .85 = 51.10 FWHP. After that I used a calculator on Wallace racing to figure my wind resistance and rolling resistance power consumption. I typed in drag coefficient of .35 (chev spark), Frontal area of 25 square feet, combined weight of 3900 lbs, and speed of 55 mph. Now I changed up the original formula here because I calculated the rolling resistance as a HP figure instead of using the RIMPULL formula that was originally suggested. The calculator I used said I needed 17.37 wheel horsepower to overcome wind (9.94 HP) and roll resistance (7.44 HP) when I typed in the above values (.35 drag, 25 ft/sq, 3900 lbs, 55 mph) on Wallace Racing Drag Calculator. So, 51.10 - 17.37 = 33.73 HP. After all these losses I am left with 33.73 Remaining Front Wheel Horsepower. The only thing left to calculate is my Grade Resistance. To calculate grade resistance I converted into the rimpull formula with my remaining HP like the post says. So for rimpull I did 377 x 33.73 = 12,716.21 Divided by 55 mph = 231.20 lbs (RIMPULL). To calculate grade resistance I used the chart posted above at 6% grade since this is likely the highest grade on the US interstates I will encounter on my trip. My combined weight with car, boat, and myself is 3900 lbs. So since my setup is 1.95 tons I multiplied 1.95 x 120 = 234 lbs required (RIMPULL) for this grade and weight. So my Original rimpull number was 231.20 - 234 = -2.8 lbs. This shows that I barely do not have enough power.

1) Started with 84 Crank HP at 6400 RPM
2) Decided to go with my Crank HP at 4500 RPM which is 72 Crank HP
3) Subtracted 16.5% power from the 72 for elevation loss at 5500 feet. (72 x .835 = 60.12 Crank HP @ 4500 RPM)
4) Manual Transmission loss of 15% (60.12 x .85 = 51.10 Front Wheel HP)
5) Wind/ Roll Resistance HP consumption of 17.37 HP. (51.10 - 17.37 = 33.73 FWHP)
6) RIMPULL Available Formula (377 x 33.73 HP = 12,716.21 Divided by 55 = 231.20 lbs rimpull force)
7) RIMPULL Required Formula [1.95 (my tons) x 120 (6% grade)] = 234 lbs rimpull force REQUIRED.
8) I am 3 lbs short of being able to maintain the speed, can someone verify this math?

My speed at 4500 RPM is 55.43 MPH in third gear. (23 inch diameter tire, 4.21 final drive, 1.32 gear ratio for 3rd, 4500 RPM= 55.43 mph)
So unless I DO encounter a 6% grade right at the highest elevation in my trip (Butte, Montana), I shouldn't have to go above 4500 RPM (3rd gear) to be able to maintain 55.
Math check anyone?

 

[stealth13777]

Your drag coefficient is off. The boat adds drag to the spark's original coefficient.


Sent from my iPhone using Tapatalk

 

[stealth13777]

You must be registered for see images attach

So how would I calculate the boat's drag?

I've never done these specific calculations, but you would need to know an 'average' coefficient for the boat I think. However, as you are towing with a smaller car, the boat's aero tendencies will have a greater effect than what is normally expected behind a larger vehicle such as a truck.

I'm hoping one of the guys above who have done this stuff will chime in, because I simply don't have the time to go through everything already posted plus my old textbooks to give you the full answer you want. My response was based on a cursory review where I did not see the aerodynamic effect of the trailer taken into account.


Sent from my iPhone using Tapatalk

 

[[email protected]]

Ok I went back to the calculator on the Wallace Racing website and typed in some other figures to try and compensate for the boat's drag like you said.
The original figures I used were .35 Drag coefficient and 25 sq/ft of frontal area, which was for the car only because I thought the boat's drag would be minimal.

I added 5 square feet on the frontal area which brought the number from 25 up to 30 sq/ft. I added 1 sq/ft for each tire, one for the boat's windshield, and 2 for the Motor.
I also increased the Drag coefficient from .35 to .50 for the setup as a guess. The calculator said that It now takes about 25 HP instead of the old 17 HP to overcome wind and roll resistance. I am not sure if the calculator I used is referencing crank or wheel HP either. If it is wheel HP then the 25 HP figure is actually more like 29 HP at the crank.
There unfortunately are a ton of drag variables but I do know one thing for certain. I know the amount can't be greater than about 30 HP required for wind and Roll resistance.

I know this because the dyno chart for my engine shows I only make 38 Crank HP at 2600 RPM. (Which is 5th gear at 55 mph).
If you want to verify this I have attempted to attach the dyno chart for my engine in the first Picture below.
I have put the vehicle in 5th gear at 55 mph and put the pedal to the floor and it slowly gains speed. So with the worst case scenario I'm guessing 30 hp max.
I'm assuming based on the slow acceleration I witnessed on flat ground in 5th gear that I had no less than 8 crank HP overcoming all the resistances.

Would you think this was a valid estimate with those variables? And does that seem to better correct the drag coefficient errors I had originally?
Below is the Dyno chart.

You must be registered for see images attach

You must be registered for see images attach

You must be registered for see images attach

You must be registered for see images attach

 

[stealth13777]

I would say that sounds pretty good. The engineer in me always prefers to err on the bad side of things. Ideally now you would find that either your calculations are correct or that you actually have a little more power than planned for; much better than not having enough.

Pics are not working btw (saw your msg), there's a tutorial on this site cause it can be finicky about letting pics work

http://www.oilburners.net/forums/sh...on-how-to-post-pictures-uploaded-to-the-forum

Sent from my iPhone using Tapatalk

 

[Waystro]

Thanks for the Awsome Read.

This should be Stickied.

 

[[email protected]]

You must be registered for see images attach

You must be registered for see images attach

You must be registered for see images attach

You must be registered for see images attach

I would say that sounds pretty good. The engineer in me always prefers to err on the bad side of things. Ideally now you would find that either your calculations are correct or that you actually have a little more power than planned for; much better than not having enough.

Pics are not working btw (saw your msg), there's a tutorial on this site cause it can be finicky about letting pics work

http://www.oilburners.net/forums/sh...on-how-to-post-pictures-uploaded-to-the-forum

Sent from my iPhone using Tapatalk

Alright I followed the guide to post the pics I wanted. Should be good now.

 

[lotzagoodstuff]

I never thought I'd see a calculation on a Chevy Spark towing a boat, but the calculations are pretty interesting. That pass in Montana is steep and long, it will be very interesting to see if the mathematical model proves accurate, but at the very least, you can optimize all the variables and see if you get your ground speed target.

Good luck!