Tech: Tires, Gears, MPH and RPM
A common 4x4 application is an upgrade to larger-than-stock tires. Once completed, this change immediately alters vehicle speed at a given rpm, rpm at a given speed, and effective gear ratio, which in turn affect both acceleration and fuel economy. Tire size, gear ratio, mph and rpm weave an intricate pattern of performance. Change one and all four are affected.; knowing any of the three, the fourth can be easily determined. The following four formulas illustrate the point:
Tire diameter = ((MPH x Gear Ratio) x 336) / RPM
Gear ratio = ( rpm x tire diameter) / (Mph x 336)
Mph = (rpm x tire diameter) / (Gear ratio x 336)
Rpm = ( (mph x gear ratio) x 336) / Tire diameter
If you are contemplating a tire size upgrade and know your rear-end gear ratio, you can measure your tire size and observe rpm and mph, you can calculate what gears are in your axles.
How To Calculate Actual Speed: With the change to taller tires, your speedometer will real "slower" than the actual vehicle speed. To determine the percentage of speedometer error, the formula is a simple relationship between old and new tire diameters.
Actual Speed = (new tire diameter x indicated speed) / Old tire diameter
Example: You’ve replaced your 30-inch OEM rubber with a new set of 35-inch all-terrains and you want to know your actual speed when the speedo reads 60 mph:
(35 x 60) / 30 = 70 mph
Speedometer ratio adjustment calculation
Ever wonder how far off your speedometer is with your new bigger tires? By using a simple ratio calculation, this info will only approximate your corrected speed and depends on the accuracy of tire size diameters (assumimg nothing but tire size has changed). If you know specific information about your vehicle (gear ratios, RPM, etc.) then use the Gear Ratio calculator, it's probably a little more accurate.
Formula used
(New Tire Diameter / Old Tire Diameter) * Speedometer MPH = Actual MPH
Another way of looking at this relationship would be to figure what the indicated speed would be if you were actually going 60 mph. In this case, the tire diameter relationship is flip-flopped to:
Indicated Speed = old tire diameter x actual speed / New tire diameter
Using the previous example, your speedometer reading at an actual 60 mph is:
30 x 60 / 35 = 51 mph
Gearing up: Using the above tire change as an example, lets say that your vehicle is currently running a 3.40:1 final-drive gear set. Now that you have changed to a taller tire, you want to determine the actual, or effective, final ratio. This can be figured by dividing the old tire diameter by the new, and multiplying by the current gear ratio (:1):
30 x 3.40 / 35 = 2.91:1
Dropping from a 3.40:1 to a 2.72:1 ratio will reduce off-the-line responsiveness and severely affect slow-speed trail capabilities. If your new 35-inch rubber is just what you want, but you now need to restore your vehicle’s low-end, the following formula will allow you to determine what gear set (equivalent) ratio should be installed to compensate:
Equivalent ratio = new tire diameter x original ratio Old tire diameter
Or, in this example:
35 x 3.40 / 30 = 3:85:1
By installing a gear set in the range of 4.25:1, you will not only restore your vehicle’s low-end responsiveness, you will likewise restore your speedometer’s accuracy.
Figuring gear ratio:
Knowing what gears are in a given axle is a must when considering that axle for a swap. The actual ratio or reference code, will normally be found on either a tag attached to a bolt, or will be stamped into the axle housing. If it cannot be found, there is a simple method for manually (and mathematically) determining the ratio for any axle installed on a vehicle.
Raise both wheels of the axle, with the transmission in Neutral. (Make sure you support the vehicle with safety stands and block the front tires.) Make a reference mark on the driveshaft and on the differential housing. Next, without rotating them, make a mark on both tires and their respective fender wells. With a friend watching the driveshaft, carefully rotate both tires at the same time exactly one revolution. The number of turns the driveshaft makes will indicate the ratio. If the driveshaft rotates 4 ½ turns, for instance, the axle ratio is roughly 4.5:1.
METRIC TIRE TO DIAMETER (INCHES) CALCULATION
Most of the formulas dealing with gear ratios will want a tire diameter (measured in inches). This formula is a quick way to get the tire diameter of those metric tires that are common on just about everything stock. For example a LT265/75R16 would be around 31.6 inches tall and 10 inches wide. Enter any three of the numbers into this form to solve for the fourth. "LT" means Light Truck and "P" means Passenger tire. The bigger number (on the left) is the Section Width. The number to the right of the slash ("/") is the Aspect Ratio (percent of width). The "R" means Radial tire and the last number, far right, is the rim diameter in inches.
Formula used
((Section Width x Aspect Ratio x 2) / 25.4) + Rim Diameter = Tire Diameter
Width in inches = section width / 25.4
Section Height in inches = Width in inches X Aspect Ratio (%)
GEAR RATIO CALCULATION
Calculating Gear Ratio
For two standard round gears, the gear ratio is calculated by counting the number of teeth on each gear and dividing the number of teeth on the driver gear by the number of teeth on the driven gear. For example, a gear with 25 teeth drives a gear with 75 teeth. Dividing 25 by 75 gives you a ratio of 3/1, meaning that for every three rotations the driver gear makes, the larger gear turns once.
If your tires are bigger than stock you either guess at the actual MPH or do something like count the seconds between mile markers on the highway while maintaining 60 on the speedometer. If you know your gear ratios and tire size you can get a fairly close number using this calculating tool. Fill in all entries except the one you want an answer to in green section only. If you'd like to find your overall crawl ratio, enter the Diff/Trans/Transfer Case ratios.
Formulas used
(RPM x Tire diameter) / (Diff Ratio x Trans Ratio x TCase Ratio x 336) = MPH
and
(Trans Ratio x TCase Ratio x Axle Ratio) = Crawl Ratio
Definition of Gearing Ratios
In the automotive industry, gear ratio refers to the difference between the input and output speed of a differential or trans-axle. The purpose of the gear ratio is to give the best combination of performance and economy for a given engine size and vehicle weight. Some gear ratios are designed to operate outside of this condition, such as those used by hot rods in drag racing.
Function
1. In the simplest terms, a gear ratio is the difference in size between two gears that have the same tooth spacing. One common ratio is the 4.10 gear ratio used in heavy-duty pickup trucks and drag-racing cars. This ratio is considered "low-geared"; for every revolution the larger gear (attached to the axles and wheels) makes, the small gear (attached to the drive shaft) makes 4.10 turns. This gear reduction gives increased power at the expense of top speed and fuel economy. An example of a "high-geared" ratio would be 2.62, where the large gear that drives the wheels turns once every time the drive shaft gear turns 2.62 times.
Effects
2. The effect of the gear ratio is to convert rotational energy--in this case coming from the drive shaft--to a desired level of energy at the wheels. The gear ratio does not increase horsepower; it merely changes how it is used. A lower ratio offers greater power while sacrificing top speed, whereas a higher ratio offers greater top speed with less power. Gear ratios also affect the vehicle's fuel economy. A higher gear ratio offers greater fuel economy on the highway, and a lower ratio will be less efficient. This is because the higher a gear ratio is, the fewer revolutions the engine has to make to achieve a desired speed. Since one of the things that affect fuel economy is engine RPM, fewer revolutions per minute use less fuel.
History
3. Gear ratios have existed since the first wooden gears were created. They were in use in applications such as windmills, where the weak rotational energy from the blades of the windmill was made usable by through slower speeds that turned a large grinding stone. Some uses predate even this. One of the simplest ancient gear ratios involves the well-bucket winch. A wooden cylinder with a handle was used to wind a rope and pull the bucket full of water up to the operator. This is an example of gear reduction, where ease of use was preferred to speed.
Considerations
4. Gear ratio changes to a vehicle can change seemingly-unrelated aspects of vehicle operation. For example, changing the gear ratio of most vehicles will cause the speedometer to register inaccurately. The gear that drives the speedometer cable is sized according to the gear ratio. This gear must be replaced to ensure accuracy of the speedometer. One of the most frequently overlooked gear ratio changes occurs with changes to tire size. While a tire is not a gear, changes to its diameter have the same effect. Putting larger tires on a car effectively increases its gear ratio, costing power and gaining fuel economy, whereas smaller tires increase power but reduce fuel economy. Tire size changes also affect speedometer accuracy.
Benefits
5. Changing the existing gear ratio can be highly beneficial if done to meet specific needs. For example, a large farm truck, or a truck used to pull a boat or trailer, can benefit from a lower gear ratio. The increased performance when stopping and starting, or going up hills, may easily outweigh the loss of fuel economy. The same is true for sports cars used in drag racing. A lower gear ratio gives more power to the wheels, at the cost of top speed; occasionally drag racers will benefit from a higher ratio, trading excessive wheel power for rotational speed. This depends on the weight of the car and the horsepower available. Many times the ideal ratio for a particular race car is not the ratio that the differential came with.
As a 'general' rule of thumb, choose green to stay close to factory gear ratios, yellow for better economy and highway usage and red for better off road capabilities.
What's in a Ratio?
An automobile uses gear ratios in both the transmission and the drive axle to multiply power. The two ratios multiplied together equal the final drive ratio. Spend a few minutes in any bench-racing session and soon you'll hear rear axle gear ratios discussed. For many performance cars, 3.73s and 4.10s are common gear choices. The rearend gear ratio refers to the relationship between the ring gear and the pinion gear. By simply dividing the ring gear tooth count by the pinion gear tooth count, the ratio is determined. For example, if we divide a ring gear with 41 teeth by a pinion gear with 10 teeth we find that the gear ratio is 4.10:1 (41/10 = 4.10).
Tire diameter will also have an effect on a vehicle's final drive ratio. As tire diameter changes, so will engine rpm at a given speed. We can demonstrate this with the simplified formula: rpm = (mph x final gear ratio x 336*) / tire diameter (*see "Formulas for Success" sidebar). For example, given 65 mph, a tire diameter of 30 inches, and a final gear ratio of 4.10, the engine speed will be approximately 2,984 rpm--(65 mph x 4.10 final gear ratio x 336) / 30-inch diameter tire. If we reduce the tire diameter to 25 inches, the engine speed increases to 3,581 rpm. By installing shorter tires, the vehicle will accelerate as though it has a 4.73 (higher numerically) gear without the expense of gear swapping.
Because transmissions are comprised of several gear choices, the transmission allows the vehicle to accelerate quickly with lower gears and to maintain a cruising rpm using higher gears. In the '60s and '70s, most transmissions offered three or four gears with a 1:1 high gear. Using a TH400 as an example, First gear is 2.48:1, Second gear is 1.48:1, and Third gear is 1:1. Multiplying the 2.48 First gear by the 4.10 rear axle results in a final drive ratio of 10.16:1 (2.48 x 4.10 = 10.16). For most street performance applications, a 10:1 final First gear ratio is usually considered optimal. The disadvantage of operating a 4.10:1 axle ratio on the street with a 1:1 high gear is excessive freeway engine speed.
Fortunately, today's transmissions frequently utilize Overdrive high gears in the neighborhood of 0.70:1, which allow reduced engine speeds. Combine these overdrive transmissions with a 4.10 axle ratio and you have a fuel-friendly final drive ratio of 2.87:1 (4.10 x 0.70 = 2.87) in high gear. A TH200-4R overdrive automatic utilizes a First gear of 2.74, a Second of 1.57, a Third of 1.00, and a 0.67 Overdrive. With this transmission's First gear ratio of 2.74 combined with a 3.73 axle ratio, the final drive ratio >> yields a 10.22 (2.74 x 3.73 = 10.22). In overdrive, the final drive ratio equates to a Bonneville-ready 2.49:1.
Making Torque Multiply
Acceleration is all about torque. One way to accelerate more quickly is to multiply the torque at low speeds to help move the vehicle forward. That's what a torque converter does. The torque converter features a component called a stator. The stator changes the direction of oil flow to the pump impeller's rotating direction and also incorporates a one-way clutch assembly. This redirection of fluid increases torque by applying the energy remaining in the oil.
By applying the basics of gear ratios and power leverage, you can easily improve acceleration without paying too steep a price in highway rpm. It's all in the ratios.
The Numbers Game
Choosing the proper gear ratio can give your car the performance you want. Remember, acceleration depends on torque. Engines that produce more torque generally require less gear for optimal acceleration.
Tire diameter plays a big role in the final drive ratio and engine rpm. Shorter tires increase engine rpm and are sometimes an economical way to improve acceleration.
Torque converters multiply torque at low speeds. If your engine produces low amounts of torque, a converter with a higher stall speed and greater torque ratio can improve acceleration. The trade-off is that a higher-stall converter slips more, which means a higher engine rpm at a given speed.
Overdrive automatics like the 4xRE series offer a low First gear and a 0.7x Overdrive. This allows the use of performance gears during low-rpm freeway cruising.
Rack-and-Pinion
A rack-and-pinion gear system consists of a round gear known as the pinion and a flat, toothed component known as the rack. The principle is the same; however, rather than rotations, the ratio determines the linear distance traveled by the rack with each rotation of the pinion.
Calculating Rack-and-Pinion Gear Ratio
Instead of counting the number of teeth in each gear, the distance the rack moves is measured in inches. Measure the distance from the end of the rack to an arbitrary point, turn the pinion one full revolution and then measure the distance again. The difference is the gear ratio.
Steering Gear Ratios
Bear in mind that adding power assist does not quicken the steering; it only decreases the input effort. Remember, also, that the steering ratio required for your car is a function of the radius of the turns of the race track, and on dirt, the slide angle necessary to steer into. In general, converting from manual steering to power assisted steering will permit quickening the steering ratio by at least one step, and usually two. Typical applications of the various rack ratios appear in the chart (Figure 8). The "ratios" (1.57, 2.09, etc.) in the chart refer to rack and pinion gearing and are given as linear inches of rack shaft travel per turn of the pinion (or steering wheel). Since the rack steers the front wheels by means of levers (the steering arms out on the spindles), the actual overall steering ratio of the car depends as much on their length as on the diameter of the pinion gear driving the rack.
How to measure the RACK ratio
If there are no numbers stamped on the caps, or if you have reason to believe a different pinion has been installed, just measure the distance from one tie rod hole (or from the end of the rack shaft) out to some stationary object (a piece of flat stock clamped to the frame rail). Turn the steering wheel (or the pinion) one full revolution and remeasure; the difference is the linear travel of the rack, which is the "gear ratio" of the rack and pinion. For reference, each additional tooth on the pinion increases the linear travel in one turn by slightly more than 1/4 inch.
How to calculate the OVERALL steering ratio
The overall steering ratio (12:1, 14:1, etc.) is measurable using turntables under the front wheels. Beginning with the front wheels pointed straight ahead, rotate the steering wheel one turn (360 degrees) one way, and read the turning angle of the front wheels from the turntable scales. You will have to resolve the difference between the right and left due to the Ackerman or steering toe; the usual method is to read the angle of the inside wheel, which is the maximum value. In road racing some prefer to average the two.
As an example, if your reading is 36 degrees, dividing this into 360 gives you a quotient of 10, and thus a 10:1 overall steering ratio (if it is not possible to get a full turn out of the steering wheel, use three quarters of a turn and divide into 270). With a six-inch steering arm, a result of 10:1 is roughly what you could expect with a 3.14 rack. This measurement becomes more approximate with quicker racks and shorter steering arms, and because of the prevalence today of rack and pinion steering in short track stock cars it is common now to refer simply to rack travel numbers.
Considerations
Using a lower gear ratio like 4.10 with normal city or highway driving results in poorer fuel economy. The vehicle isn't utilizing the power exerted by the drive shaft, but it is having to generate it instead. It is suggested to have a higher gear ratio for typical driving to save on gas.
A good gearing/tire combo calculator, created by Roy Grimm, is available on the web, found here: http://www.grimmjeeper.com/gears.html
He states:
This form allows you to calculate final drive ratios as well as see a comparison of speeds and RPMs within operating ranges of the vehicle. This calculator is useful for planning your rig, allowing you to see what kind of performance to expect from different combinations.
