• 4WD Math


    Offroading20150616IN my early days of four-wheel driving, I got so caught up in the excitement of getting into gear, stomping on the accelerator and crossing an obstacle. But as time went by, I encountered some horrific memories, similar to my childhood experience with mathematics and compounded equations. It’s more of a fear of the unknown more than anything, but eventually I had to tackle matters head on. So in this article, we will be dealing with some basic 4WD mathematics and how it affects your off-roader’s performance.

    Effective gear ratio
    In layman’s term, it is the change that happens to your final gear ratio once your 4WD changes to a taller tire size. For example, a vehicle with a stock 29-inch diameter tire size with a 3.5:1 final drive axle ratio will perform like it has a 3.11:1 final drive ratio when its tires are upgraded to 33 inches. When this happens, the vehicle will lose acceleration and towing capability, but it will have a lower engine revolutions per minute (RPM) at high road speeds, translating to better fuel economy in highway driving.

    In off-road driving conditions, however, the vehicle’s tire will be spinning much faster on slippery conditions, making the tires lose traction. Also, low rpm torque is lost. This will require a 4WD vehicle to attack an obstacle with more speed that could result to less control of the vehicle.

    The formula to compute the effective gear ratio is the old tire diameter divided by the new tire diameter, multiplied by the original final drive, equals the effective final drive ratio of the vehicle.

    Engine RPM at speed
    As mentioned earlier, the engine of a vehicle with a standard effective ratio but fitted with larger-diameter tires will experience a drop in engine speed when travelling on a highway.

    If you are conscious about your vehicle’s fuel economy, the formula below is important for those who have changed the diameter size of their vehicle’s tires. The formula below is also useful for owners of non-4WD vehicles: Miles per hour multiplied by the total gear ratio, then multiplied by 336. Divide the result by the tire diameter (in inches), then add the result with the engine RPM.

    Equivalent ratio
    To bring your vehicle to a close estimate of what your “stock” effective gear ratio (which is a compromise between great off-road capability and mediocre off-road performance) is after installing taller tires on a 4WD, remember that a bigger rolling mass (taller and wider tires) will reduce acceleration regardless of ratio changes. So if it’s improved off-road performance you are after, then a numerically higher ratio is what you should go for. The formula is: New tire diameter divided by the old tire diameter. Multiply the quotient with the old ratio to get the new effective gear ratio.

    Formula for speed correction
    This formula is essential for those who are concerned about getting caught for speeding in the country’s leading expressways like the NLEX, SLEX, TPLEX and SCTEX. Special mention to Davao City where speeding is quite vigorously enforced (No pun intended here. I’m all for it). Installing taller tires on your vehicle will make it go faster than what the speedometer indicates. For vehicles equipped with an overdrive gear (in some vehicles, the top gear may be just an overdrive gear), the overdrive gear is expressed as a fraction of 0.8:1.

    So the formula to compute speedometer correction (changing of tires only): New tire diameter divided by old tire diameter, then mutiply the quotient to the sum of the indicated speed (mph) and the actual speed (mph).

    For speedometer correction (tires and final gear ratio change): Get the indicated speed then multiply it with the quotient of the new tire diameter over the old tire diameter. Get the result and multiply it again with the quotient between the old gear ratio over the new tire diameter. The result will be the actual speed.

    To get final drive ratio when overdrive is engaged: Overdrive gear ratio multiplied by the axle ratio, equals the final drive ratio

    Had enough off-road math for today? Think of this as basic arithmetic for 4x4s. Later on, we will deal with more advanced mathematics in off-road driving. Now tell me if off-roading is not for geeks. Happy trails to all!


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