Let's Geek out together - Engineers and physicists wanted

[sroodtuo]

I’ve been thinking about the effect of larger tires (weight and diameter) on a vehicle’s torque and HP to the wheels. I wanted to calculate some “real world” numbers that would identify the actual effect that increasing tire size would have on my vehicle. I came across the following formula on a physics forum that calculates the energy required to rotate one wheel, based solely on weight, to a speed of an arbitrary 60 MPH.

"Suppose the moment of inertia of each wheel (rim plus tire) is I = (3/4) m R2
where the 3/4 is a coefficient related to how the mass is distributed radially, and R is the rolling radius.

The energy of one wheel rotating at a velocity of w (in radians per sec) is
E = (1/2) I w2 = (3/8) m (Rw)^2

But Rw is just the velocity of the rolling wheel with radius R, so Rw= v (meters per sec). So for one tire, the energy is E = (3/8) m v2

For a wheel (rim plus tire) mass of X pounds (X Kg) and 60 mph (26.8 meters per sec)

E = (3/8) (X) (26.82^2) = Y Joules

1 joule = 1 watt
1 watt = 0.00134102209 horse power

If we had to accelerate four wheels from 0 to 60 mph in 4 seconds, the power would be P = 4 x Y Joules/4 sec = Z watts = HP, INDEPENDENT of rolling radius!"

Reference https://www.physicsforums.com/threads/calculating-torque-hp-losses-from-wheel-choices.334984/

I used the specs for the BFG AT KO2 in several sizes and plugged them into the formula above for comparison sake. I came up with the following:

LT265/70R17/C 31.6 “ 45.7 lbs (20.73 kg)
E = (3/8) (20.73) (26.82^2) = 5596 Joules
5596 / 0.00134102209 = 4.17 HP

LT265/70R17/E 31.6” 53.4 lbs (24.22 kg)
E = (3/8) (24.22) (26.82^2) = 6533 Joules
6533 / 0.00134102209 = 4.87 HP

LT275/70R17/E 32.2” 55.4 lbs (25.13 kg)
E = (3/8) (25.13) (26.82^2) = 6779 Joules
6779 / 0.00134102209 = 5.08 HP

LT285/70R17/E 32.7” 58.1 lbs (26.35 kg)
E = (3/8) (26.35) (26.82^2) = 7108 Joules
7108 / 0.00134102209 = 5.30 HP

34x10.50R17/D 33.5” 55.1 lbs (24.99 kg)
E = (3/8) (24.99) (26.82^2) = 6741 Joules
6741 / 0.00134102209 = 5.03 HP

Based upon these numbers alone, it appears to me that the least expensive tire size larger than stock in terms of horsepower loss is the 34 x 10.50.

I realized at this point that I have officially lost my mind and need to get a hobby. Nevertheless, I am still interested in understanding the effects (in numbers) of tire size on HP and torque.

Here’s where you come in... realizing that weight is only one component leading to a loss (or gain) in HP and/or torque, how do I account for the change in tire diameter? We can deal with tread width, rolling radius, etc. later.:blah:

Come one 1Engineer, show yourself. I know you’re out there :yield:

 

[Jeremy556]

Looks like you forgot rolling resistance. Pretty sure my 305/70/17 MTRs consume at least 100hp to produce sound above 35mph.

 

[Friggin Idiot]

That's per tire right? So you'd need 4x that amount.

 

[lightspeed]

...and the question is:
What was the name of the bus driver?

 

[1engineer]

What do you really want to know? I'll be happy to answer but I need to know what you want. Specifically.

 

[bjohnston115]

Formulas are great and dandy but also remember all of those calculations only hold true in a vacuum, not the real world (unless you add those factors in).

With my other rig (92 land cruiser) i experimented with stock 31's and several different sized 33's. The difference in pickup and gas mileage was pretty much negligible in my case, it really changed when i went to 35s without a re-gear though. I didn't notice a difference between 10.5 and 12.5 width for gas mileage either. In theory, the real issue is the gearing. If you put on 35 inch inner tubes or 35 inch concrete forms it will mess with the gearing and driving characteristics of the truck no matter what.

 

[DAGNABIT]

If you have to think this detailed about larger tires on a 4runner you really need to sell it and buy a prius

 

[Jhalko]

If you have to think this detailed about larger tires on a 4runner you really need to sell it and buy a prius

Easy now, this is ten times more interesting than some of the other new threads created this week. :nicethread:

 

[NORTHERN]

Is this at sea level or at elevation ?

 

[DEERUNNER]

Using your numbers the difference in HP between the 265 and 285 tire is 1.13 HP. Not a significant difference to me and not something I would worry about. Go big and go wide!

The answer is: Train B would arrive 20 minutes before Train A.

 

[USKTog]

Using your numbers the difference in HP between the 265 and 285 tire is 1.13 HP. Not a significant difference to me and not something I would worry about. Go big and go wide!

The answer is: Train B would arrive 20 minutes before Train A.

Modified your answer, for correctness:

The answer is: Train B would arrive 20 minutes before Train A, at station M (on the opposite side of town). lol

 

[sroodtuo]

If you have to think this detailed about larger tires on a 4runner you really need to sell it and buy a prius

I see this thread as yoga for the brain. Nothing more. It's an opportunity to stretch and exercise the brain or a chance to wear spandex and fart in public. Your choice :hippie:

What do you really want to know? I'll be happy to answer but I need to know what you want. Specifically.

I appreciate your willingness to humor me. If possible, I'd like a plug and play formula to identify the cost, in terms of HP and torque, for a given tire. I'd like it to take into account only tire diameter, weight, and tread width.

I realize their are many many "other" factors (tread compound, tread pattern, road surface, environmental factors, etc) that would also affect HP and torque but I like to start small and go from there.

 

[Canon_Bob]

You forgot to contemplate prevailing wind direction and the effect of the average number of bug strikes at varying speeds.

 

[1engineer]

I appreciate your willingness to humor me. If possible, I'd like a plug and play formula to identify the cost, in terms of HP and torque, for a given tire. I'd like it to take into account only tire diameter, weight, and tread width.

I realize their are many many "other" factors (tread compound, tread pattern, road surface, environmental factors, etc) that would also affect HP and torque but I like to start small and go from there.

Alright. Let me think about it a bit.

 

[LNBright]

...and the question is:
What was the name of the bus driver?

Leslie! (BTDT one...)

 

[IronManKansas]

I would hate to reinvent the wheel... So I found this site that covers a lot of physical dynamics for tires. Skimming over the content you should be able to get a more accurate estimate of I to determine your hp loss taking into account size and weight of your tire options . The Effects of Rotational Inertia on Automotive Acceleration
Cheers:cheers:

 

[1engineer]

Getting ready to go on epic road trip. 2500 miles in six days covering ten states in the 4Runner so I will only check in sporadically.
For HP and torque you should only need a small graph of mass and HP as this is a linear function. Easy to extrapolate.
For other losses it gets a bit more complex. For example the windage loss going to a larger tire will depend on the tread pattern and especially the differential size between stock and new tire. Height and width. That function will be cubed so twice the speed would equal 8X HP to move those bigger tires through the air.
Rolling resistance needs to be calculated also.

In reality I would think a different, measurable metric would be a better way to determine the effects of a larger tire on the 4Runner. Efficiency in loss of mpg is measurable over time and can be calculated and then measured for verification. My thoughts.

 

[philsey]

... or just buy P-rated in stock size. Easy peasey, nice and cheesey. No mental masturbation required.

Safe travels, Greg.

 

[jwkilgore]

:nicethread:

I appreciate your willingness to humor me. If possible, I'd like a plug and play formula to identify the cost, in terms of HP and torque, for a given tire. I'd like it to take into account only tire diameter, weight, and tread width.

I realize their are many many "other" factors (tread compound, tread pattern, road surface, environmental factors, etc) that would also affect HP and torque but I like to start small and go from there.

Not gonna happen; way too many variables. You've got the basics right. Based on pure mass, the "3/4" factor can vary quite a bit, but it won't be significant. The factor would be 1.0 if all the mass were at the tread; 1/2 if the mass is evenly distributed in a solid disk; and less than 1/2 if more mass is nearer the hub.

The biggest problem is that your "start small" approach is too small. Other factors have significantly more effect that pure mass, which only affects acceleration from a stop. If you accelerate to zero then drive 300 miles before stopping, the tire mass will have negligible affect.

Other factors that affect HP loss far more than pure inertial resistance:
- Rolling resistance. Unless the tire industry standardizes on a single value (resistance against turning at a set weight and set pressure), this is totally unknown. Your vehicle would have to weigh exactly the same as the test vehicle and you'd have to be aired to the same pressure. In general "highway" tires are designed for reduced rolling resistance while mud-terrain tires are designed purely for off-road traction and have high rolling resistance. All-terrain tires are a compromise. Two different tires with the exact same weight and dimensions could have significantly different rolling resistances depending on the tread pattern and sidewall flexibility.
- Larger diameter means torque loss requiring you to give it more gas to get the same results. This is all about the driver. If you accelerate hard, drive really fast against wind resistance, or pull trailers at high speeds, then this will be a huge factor. If you drive easy it won't be as important.
:driving:

 

[Antman]

Bigger tires = need mo power. Got it.:brick: