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Corsair

Posted 2021-06-05 9:27 PM (#612483)
Subject: Gear Ratio Calculation

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Posts: 43

In advance, I apologize as this topic is not strictly a FL concern. So if moderators want to move this somewhere else, please do.

Anyway, so I have a math issue. My buddy and I are working on a truck project and we are trying to figure out what gear ratio we need in order to tow/haul 10,000lbs and try to have the best possible fuel economy. We don't need it to be good off the line, we just need it to move and not damage the engine/drivetrain.

So let's use a hypothetical scenario and numbers. We need to move 13000lbs. (3000 actual vehicle weight and towing 10,000lbs). We have an engine that makes 200 hp and 200 lb-ft of torque (I'm assuming torque is the more important number here) @ 3000 rpm. Let's say we have a torqueflite tranny with a 1st gear of 2.45 and 1 to 1 final drive. We have 28" diameter tires. We will never ascend/descend a grade of more than say 5% (not sure what the maximum grade for a highway is). We need to maintain a minimum top speed while towing of 55 mph. So, what is the math equation and/or other information I need to figure this out?

I have been looking around the internet and have not found a direct answer to this question. I figure some of you here, have figured this out before.

Edited by Corsair 2021-06-05 9:28 PM

56D500boy

Posted 2021-06-06 2:33 AM (#612486 - in reply to #612483)
Subject: RE: Gear Ratio Calculation

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.
This is not the answer that you are looking for but:

Assuming the wheels are 15" with 235/75/15 tires, the overall diameter is 28.88 inches.

With a 3.54:1 rear diff and 1:1 top gear (same for a Torqueflite as a Powerflite), 3000 RPM would give you a calculated 72.8 mph

Same situation but with a 3.31:1 rear diff, 3000 RPM would give you a calculated 77.8 mph.

But really, I doubt that a 3000 lb vehicle has any business towing 10,000 lbs of anything.

For one thing, the 3000 lb vehicle's brakes are very likely to be inadequate for the job unless you have electric brakes on the trailer that you can use.

I think you need a decent truck:

https://tap.fremontmotors.com/choosing-pickup-truck-to-pull-tow-9500...

Corsair

Posted 2021-06-06 4:18 AM (#612487 - in reply to #612486)
Subject: RE: Gear Ratio Calculation

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Posts: 43

For reference, the truck in question is my buddy's '61 land rover (well, one of them anyway) and all that it has to offer in terms of power... I can say that I witnessed the poor old gal pull a 10,000lb trailer full of coal once (before it broke the crankshaft... and the transmission... and the rear axle shaft...)

This is actually the problem I'm trying to figure out. No where on the internet actually explains the math behind this topic. I am well aware of generally what you need to haul stuff. But much like a gear ratio calculator, I figure there is some math formula that calculates towing capacity, yet the internet seems tight lipped on what it is. The engineers that design trucks certainly start with a formula or set of formulas to figure out the mechanics of their drivetrains. I want to know those equations. I'm not asking for a safe towing capacity. I'm asking for a theoretical math formula, in short, even if it does have a bunch of variables.

Much like with a gear ratio calculator, if you put larger diameter tires or a lower diff gear you now have ridiculous high end speeds, that you will never actually attain. Older trucks hauled thousands of pounds of cargo and yet they only had engines that made like 100 hp with 3 or 4 speed transmissions. They just had top speeds of 50 or 60 mph. So, by that logic, give these trucks more powerful engines and lower rear gears and now they can go 90 or 100 mph (not considering factors like wind resistance). What is the math formula for figuring this out? I mean my 800lb lawn tractor can pull around my '57 dodge, but only in first or 2nd gear at about 2 mph, it literally won't move in a higher gear.

I feel like I'm hovering around what is probably an easy, obvious answer and yet I can't figure it out. I'm thinking its something to do with torque multiplication and the power to manipulate rotational motion, I just can't figure out the relation. Really, all I need to figure out is the power needed to start moving from 0 mph, everything after that is all about staying in the engines power band, I suppose. If only I had gone to college for mechanical engineering...

Powerflite

Posted 2021-06-06 11:31 AM (#612494 - in reply to #612483)
Subject: Re: Gear Ratio Calculation

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The math is quite simple. The problem is that it depends on many variables that you probably have no idea what they are. In the end, it is best to make your best judgement and give it a try. Hence the total awesomeness of the Ford 9" and Chrysler 8 3/4, because you can swap gears around with ease.

In general, you will realize the best fuel mileage with the lowest rpm you can run at without lugging the motor or causing pinging. Therefore, you must know the torque curve of your motor in question to know how that varies with rpm. Once you have that, you can calculate the total forces acting on that motor at a given speed and check to see if the torque from the motor is enough to overcome it.

Ftotal = Fr + Fs + Fa , where Fr = drag due to rolling resistance, Fs = drag due to gradient slope, & Fa = aerodynamic drag
The rolling resistance depends on how many wheels are rolling, and how much weight is on each wheel. But theoretically, you can estimate it as being all on one wheel with:
Fr = c*m*g, c= .015 to .02, m= mass in Kg, g = 9.81 m/sec^2 (if you want english units, I recommend just to convert them at the end)
Fa = Cd*Af*p*(v^2/2), where Cd is the drag coefficient (approximately = 1.0 for a truck), Af = frontal area, p = air density, V= velocity
Fs = m*g*Sin(A), where m=mass, g=9.81 m/sec^2, A= angle of incline

Then to compare the total force to the torque available:
e*Tq*GR/r > Ftotal, where e= drivetrain efficiency (approximately .8), Tq = torque from your motor at that rpm, GR = final gear ratio (including transmission & rear axle), r = tire radius (diameter/2)

This is the math required, but as you can see, there are a lot of unknowns here that you would have to estimate.

Edited by Powerflite 2021-06-06 11:42 AM

58coupe

Posted 2021-06-06 12:11 PM (#612497 - in reply to #612483)
Subject: Re: Gear Ratio Calculation

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Why don't you start by figuring out what gear ratio is in the Land Rover and explaining why it isn't OK as is. If you only want to pull this weight occasionally it may be fine as is.

56D500boy

Posted 2021-06-06 12:34 PM (#612498 - in reply to #612487)
Subject: RE: Gear Ratio Calculation

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Corsair - 2021-06-06 1:18 AM
For reference, the truck in question is my buddy's '61 land rover (well, one of them anyway) and all that it has to offer in terms of power... I can say that I witnessed the poor old gal pull a 10,000lb trailer full of coal once (before it broke the crankshaft... and the transmission... and the rear axle shaft...

Umm...

From Britain:

"What weight can a Land Rover tow?

Maximum speed limit while towing is 60mph on the motorway and 50mph on A roads. Maximum towing capacity for an unbraked trailer is 750kg. Maximum towing capacity for a braked trailer is 3500kg, but this depends on your vehicle and when you passed your driving test."

10,000 lbs = your buddy needs a bigger truck or a smaller load

Corsair

Posted 2021-06-06 10:09 PM (#612504 - in reply to #612494)
Subject: Re: Gear Ratio Calculation

Member

Posts: 43

Powerflite, that is the math I was looking for. Thank you.

My buddy's rather comical truck issue was simply the mental catalyst that got me thinking about this and took me down this rabbit hole.

Stroller

Posted 2021-06-15 10:49 AM (#612791 - in reply to #612483)
Subject: Re: Gear Ratio Calculation

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Well the math for me goes is what is the rated towing for the vehicle. Many folks use under powered vehicles to do stuff for better gas mileage. Like a 318 in a 1/2T pickup expected to handle a 32 foot fully loaded travel trailer. Personally I would not use a 3,000 lb 200hp vehicle to haul a 2,000 lb trailer with a 4,800 lb vehicle on it. It would do it, but it would not like it. Especially out on a highway.

Chrome58

Posted 2021-06-16 2:21 AM (#612822 - in reply to #612504)
Subject: Re: Gear Ratio Calculation

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Corsair - 2021-06-07 4:09 AM

Powerflite, that is the math I was looking for. Thank you.

I'm nitpicking, but this is not a math problem (nor a math solution that was given), but a physics one.

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