When to shift: why the best shift point is past peak torque

Peak torque is the wrong place to change gear. The next gear multiplies torque by a smaller number and drops the revs to a lower point on the curve. What counts is the force at the wheels before and after the shift. This post finds the point where the two are equal, using the invented engine from the dyno chart post and two invented gears. None of it is data about a car in a game.

The rule

Force at the wheels is proportional to engine torque multiplied by the overall gear ratio (the gear times the final drive, as in the gear ratio post). Losses and tyre radius apply to both gears equally, so they cancel.

Changing up from one gear to the next at engine speed r drops the revs to r × (next ratio ÷ current ratio). The best moment to shift is when the force afterwards equals the force before:

torque at r × current ratio = torque at (r × next ratio ÷ current ratio) × next ratio

Before that point, staying in the current gear gives more force. After it, the next gear does. The point is where the two wheel-force curves cross.

An example pair of gears

Take the dyno chart engine (torque 220, 260, 290, 300, 280 and 240 lb-ft at 2,000 to 7,000 rpm, joined by straight lines) and a 3.42 final drive with 26-inch tyres. Gear A has a ratio of 1.30 and gear B a ratio of 1.15, both invented. The overall ratios are 1.30 × 3.42 = 4.45 and 1.15 × 3.42 = 3.93, so shifting from A to B drops the revs to 1.15 ÷ 1.30 = 0.885 of their value. Redline is 7,000 rpm. Road speed is mph = rpm × 26 ÷ (overall ratio × 336).

Solving for the crossover

Between 6,000 and 7,000 rpm the example torque falls in a straight line, 280 − 0.04 × (rpm − 6,000). Setting the two sides of the rule equal gives a shift at 6,898 rpm in gear A. Revs then drop to 6,898 × 0.885 = 6,102 rpm in gear B. Check it:

• Gear A at 6,898 rpm: 244.1 lb-ft × 4.446 = 1,085.2.
• Gear B at 6,102 rpm: 275.9 lb-ft × 3.933 = 1,085.2.
• Both correspond to 120.1 mph.

The torque peak is at 5,000 rpm. The crossover is 1,898 rpm above it, so the best shift is well past peak torque. It is also past the power peak, which with straight lines between the points is at about 6,500 rpm (the dyno chart post shows it lies between 6,000 and 7,000).

Why equal force means equal power

At one road speed the wheels turn at the same rate in either gear, so force at the wheels is proportional to the power the engine delivers. At the crossover the engine makes 244.1 × 6,898 ÷ 5,252 = 320.6 hp in gear A and 275.9 × 6,102 ÷ 5,252 = 320.6 hp in gear B. So the rule can be read off a horsepower curve: shift when the power at the dropped revs equals the power you are leaving. The two rev figures sit either side of the power peak.

What an early shift costs

Here is the force just before and just after a shift at four engine speeds in gear A, shifting into gear B:

• 5,000 rpm (peak torque): drops to 4,423 rpm, 1,334 becomes 1,157, a loss of 13.2%.
• 6,000 rpm: drops to 5,308 rpm, 1,245 becomes 1,156, a loss of 7.2%.
• 6,500 rpm (about peak power): drops to 5,750 rpm, 1,156 becomes 1,121, a loss of 3.0%.
• 7,000 rpm (redline): drops to 6,192 rpm, 1,067 becomes 1,071, a gain of 0.4%.

The later the shift, the less it costs, until the crossover. Past it, staying in gear A gives up force.

When the crossover is beyond the redline

The gap between gears decides it. The four-speed in the gear ratio post has steps of 2.80 to 1.80, which drop the revs to 0.64 of their value. Checked against this engine, the curves do not cross anywhere below 7,000 rpm: the engine runs out of revs first. The right move there is to shift at the limiter. Close gears, like the 1.30 and 1.15 above, bring the crossover into range.

Limits of the method

• The shift itself takes time. The comparison assumes no gap in drive, and a real change costs a moment of no push at all.
• Grip can cap the force. If the tyres cannot pass on the force, extra ratio only adds wheelspin. The launch RPM post covers that limit.
• The real curve bends. Straight lines between six points are an approximation, so treat 6,898 rpm as an estimate.

Using it in the game

Pink Slip Kings has manual shift controls, a dyno that compares horsepower and torque, and adjustable gear ratios and final drive. Estimate where the dropped revs land, then check the result on the time slip. What suits any particular car in the game is outside this post.