Back to School: Do the Math - Transmission Digest

Back to School: Do the Math

It is now back to school season and that brings to mind the difference in education standards in our society. When I went to school all of my teachers (New York City Public Schools) knew their subjects inside out. If you didn’t do it right, you did it over, and that could include being left back to do a whole year over. We learned math, English, geography, history, civics and social studies, plus very active physical training. We had very little obesity, everyone could write in script and print, and everyone read to the best of their ability.

Up To Standards

  • Author: Mike Weinberg, Contributing Editor
  • Subject Matter: Numbers crucial to survival

It is now back to school season and that brings to mind the difference in education standards in our society. When I went to school all of my teachers (New York City Public Schools) knew their subjects inside out. If you didn’t do it right, you did it over, and that could include being left back to do a whole year over. We learned math, English, geography, history, civics and social studies, plus very active physical training. We had very little obesity, everyone could write in script and print, and everyone read to the best of their ability.

Enter the modern day product emanating from the high schools of today, and students seem ill prepared for a productive life in the real world. GM, Ford and Chrysler, as well as many other manufacturers, are spending hundreds of millions of dollars to teach their new hires fractional math, basic reading skills, and company policy. Advanced math may not be needed beyond school, but I see many kids today that cannot make pocket change or control their money.

Some relatively easy math will help us succeed in our business. Shops will be tested for this by their customers every day. Ratios, speedometer calibration, metric-to-English conversion and reverse, and basic fractional math are used on a daily basis. We will look at these basics that are required for survival of the fittest in our world of auto repair. First we will look at simple English/metric conversions. Most good electronic digital vernier calipers and micrometers can do this for you but it is nice to have some of the formulas available so you can function with a dead battery.

Ratios need to be understood and determined to enable the technician to make the customer understand the effects of certain changes they make to the vehicle. Transmission changes (ratio), tire sizes, and rear-end ratio changes create major differences in engine rpm and usable torque, speedometer calibration, drive-shaft speeds, and will alter the drivability significantly. It is critical to make the customer aware of the difference in the vehicle before repairs are made so that we have a happy outcome.

Suppose you are going to swap a used unit for a customer who can’t afford a rebuilt. Sometimes you can just swap the speedometer gear from old to replacement unit and things will work fine. In other cases the drive gear is different, so you have to find the ratio for the drive and driven gears. Most of the time the replacement unit will have a different drive gear than the original.

The answer here is to establish the speedometer gear ratio. The customer’s unit had a 7-tooth drive gear and a driven gear with 21 teeth. The junkyard special has an 8-tooth drive gear, so one would divide the 7 tooth by 8 – the number of teeth on the replacement – and get 0.875. Dividing the old driven gear of 21 teeth by 0.875 and we get 24, so a 24-tooth driven gear will make the speedo calibration correct.

Another major speedometer issue is caused by customers who change rear-end ratios and or increase tire sizes. This is a major business plus for you when dealing with Jeep owners who have a tendency to make those changes either for off-road use or bragging rights. See the accompanying charts for both types of Jeep speedo gears that covers 1955 through 2006, furnished by Quadratec, a supplier of Jeep accessories. The charts cover tire sizes from 27” to 44” so the recalibration is simple.

The following formulas are simple and will help you educate a customer who is changing a rear-end ratio and/or tire sizes to understand changes in engine rpm and vehicle miles per hour. We need to first establish the loaded tire radius, because there is a difference in the tire radius on the side that is loaded with vehicle weight. Measure from the centerline of the axle to the ground and multiply it by 2. MPH=engine rpm X tire diameter divided by 336. Engine RPM = MPH X Gear ratio X 336 divided by tire diameter.

Now the customer can have a clear picture of how much his shift points and torque curve will change before he spends to make sure the results are what they desire.

Transmission ratios

The next area of mathematics is transmission ratios. The arithmetic involved is very simple, but there are some pitfalls. We need to establish a ratio for every gear in the transmission, which we will arrive at by dividing the tooth count of the drive gear into the tooth count of the driven gear. Make sure you understand this clearly because many modern transmissions have overdrive gears that are on the countershaft, and they become the drive gear in the powerflow. You will wind up dividing a smaller number by a bigger number, and the ratio will always be less than 1, which is overdrive. We must first establish what the input ratio to the transmission is by dividing the input tooth count to the driven gear tooth count on the counter gear (cluster).

Example: The input gear has 19 teeth and the counter gear has 29 teeth – 29 divided by 19 gives us an input ratio of 1.52 to 1. First gear has 34 divided by 18, which gives us 1.88-1 which we now multiply by the input ratio 1.52, and we have a 2.85 1st gear ratio. 2nd gear will be 25 teeth divided by 20 which equals 1.25, multiplied by the input ratio of 1.52=1.90 2nd gear ratio. 3rd gear is 21 teeth divided by 24 teeth and we have 0.87 as the speed gear ratio which is then multiplied by 1.52 input ratio producing a 3rd gear ratio of 1.32 to 1. 4th gear is a one-to-one ratio as the input is directly connected to the output shaft with no power flowing through the counter gear. There are transmission designs where 5th gear is one to one (direct drive), so be careful to examine the layout of the gear train before you start your calculations.

So far we know the output ratios of the transmission and we now have to find the vehicle overall ratio, which means we need to find the gear ratio of the rear end. If we know that the rear ratio is 4:10, we now multiply that by the transmission ratios to get an overall ratio for each speed. 1st gear 2.85 X 4.10=11.68 overall ratio in 1st gear. Let’s look at an overdrive 6th gear that is 0.62 x 4.10 and the overall ratio in 6th is 2.54-1. It is now easy to comprehend why the engine rpm is so low in 6th as compared to 1st gear.

Business math

The next math problems involve the ability to stay in business so that you can use the previous set of formula on a steady basis. This math involves what to charge for your work, and to understand what your real gross profit is on parts and labor. Gross profit is defined as what you made selling a part before your overhead is accounted for. It involves your cost for the product, how much you mark it up to the customer, and what your gross profit margin is on the part. The problem is that markup is always more than margin unless you know how to do the math. If you buy a part for one dollar and mark it up 25% (1.00X1.25) you will have a sale price of $1.25. Your margin on that part however is NOT 25%, but 20%.

The accompanying chart will give you the sliding scale of markup to margin. If you wish to make 50% on a part, it has to be marked up 100%. If you wish to make 100% on a part it, has to be marked up 200%. In order to stay in business, you must make a minimum of 40% margin on anything you sell. That does not mean every part has to be sold for a minimum of 40% margin, but you should try to have the total parts margin in any job average out to 40% or better. This means that you can have very large markups on some parts and smaller markups on other more expensive items.

I have always been questioned as to how it is possible to sell over the manufacturer’s list price. What is a list price or MSRP (manufacturers’ SUGGESTED list price). Where does the list price come from? It is set by the manufacturer as a suggestion. Who is the manufacturer, if not your biggest enemy in business apart from your government? They set a list price, which by federal law is only a suggestion. They then give you a professional discount of 10%, 15% 25% from list price when you buy the parts from them. Can you live on that and stay in business? Look at the list price of parts in the vehicle that is their suggestion and add up what it would cost to buy all the parts in the car, and you will see that a $20,000 car would cost $100,000 with no labor to put it together. The same thing occurs every day selling cars, where the easy-to-get models are discounted by the dealer and the hard-to-get models are sold well over the MSRP by the dealer.

You are giving your customer value added by providing the correct parts. You obtain the parts, which in some cases means going to get them physically, you pay the freight for them to come to you, you lay out money extending credit to your customer, and collect when the job is complete. Your customer does not want to lose a days work chasing parts even if they had the expertise to do so, and perhaps they don’t have the money to pay for them until the repairs are complete. All the fractional math and ratios you will work with won’t mean a thing if your profit margins are not enough to keep you in business.

Mike Weinberg is president of Rockland Standard Gear.

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