987.2 Base Boxster Power Curve and "Optimal" shift points

Optimal shift points calculated and visualized! I used my previously digitized the power/torque curves for the Base and combined them with my understanding of the gear ratios of the Base. I used Claude to calculate the optimal shift points , and the graphs and insights are intriguing. I welcome comments! (Note I'm using the factory curves but allowing for a +200rpm increase from a tune. I dont have the tuned curves so i cant do that until I get that. The +200 didn't affect the calculated shift point much at all, but perhaps they might with the tuned curve. Clause must have extrapolated the curve beyond 7500) First, the pretty graphs: The methodology: at any vehicle speed, the optimal gear is whichever one puts the engine at the highest point on the HP curve. The shift point is the RPM at which the next gear's HP after the ratio drop exactly equals the current gear's HP — any higher and you're leaving power on the table. Optimal shift points — Boxster 2.9L (tuned, 7,700 rpm redline): Shift Shift RPM Vehicle Speed HP at shift 1st → 2nd 7,529 rpm 41 mph 167 hp 2nd → 3rd 7,329 rpm 72 mph 205 hp 3rd → 4th 7,020 rpm 101 mph 230 hp 4th → 5th 6,908 rpm 123 mph 236 hp 5th → 6th 6,935 rpm 144 mph 23 Shift points fall well below redline for every gear except 1st. That's because the HP curve peaks at 6,400 rpm and rolls off sharply. The ratio drops for 3rd through 6th (all relatively close together) land you at ~5,600–5,900 rpm after the shift — right in the fat part of the curve — so the crossover happens before you reach redline. The 1st→2nd shift is the most aggressive at 7,529 rpm. First gear has the largest ratio drop (3.667→2.050 = 0.559×), so the RPM fall is enormous. You need to be very high in 1st to land in a good spot in 2nd. 4th and 5th shift points are almost identical (~6,900–6,935 rpm). Those gears have nearly the same ratio step (1.133→0.972→0.822), so the crossover logic is nearly symmetric.

235 is the hp at the 5>6 shift

That’s very cool!! Thanks!!!!

Claude used the "equal power cross over method" not the "area under the curve method. I wasn't familiar with the former... I'm going to look at how those methods compare...

Gear Crossover shift Area-max shift Δ RPM Δ area 1→2 7,529 7,691 +162 +22,864 2→3 7,329 7,601 +271 +33,552 3→4 7,020 7,394 +374 +41,723 4→5 6,909 7,302 +392 +17,564 5→6 6,936 7,261 +325 −8,619 6 — — — −65,654 Total 3,117,554 3,159,325 +41,771 (+1.34%) The area method shifts significantly later in every gear , and the total area gain is real but modest (+1.34%). To me this makes intutive sense, shifts closer to redline especially in 1st and 2nd gear. The big graph below shows the different shift points clearest.

Wow that's a lot of graphs and charts. Too much for my old brain. I just shift by how the car feels, the conditions and what I want to accomplish.

Nice work! I always thought that shifting should be done at the peak of the torque curve to get the most power from a particular gearing, as the torque drops after its peak. It would seem that the higher revs above peak torque would only serve to over rev the engine with diminishing returns. Am I wrong?

Great analysis and data presentation. I have a few general comments/queries as someone new to this type of analysis. The analysis is based primarily on engine power. A car's top speed is determined primarily by an engine’s power output — specifically peak horsepower. So why does it matter if you match power at the crossover points? Why does it matter if "you're leaving power on the table" through the gears? "Optimising" shift points through the gears would seek to maximise acceleration, wouldn't it, extracting the best performance? As acceleration depends primarily on torque , why isn't an analysis based on torque rather than power?

I'm not an expert, but applying my high school physics: Torque is rotational FORCE and horsePOWER is FORCE * DISTANCE / time. So POWER = FORCE * RPM (rotational distance over time) We want to take into account the speed of the engine (RPM) when calculating shift points. What the "Equal Power Crossover Method" is doing is just calculating when the power after your shift is equal or higher than the power before the shift. I didn't show the torque and power curves here (in another of my posts) but its important at what rpm the engine makes a given amount of torque. an engine with 200ftlbs of torque at 7000 rpm makes double the power of an engine that makes the same torque at 3500RPM. This is good because you can just use a 2:1 gear at 7000RPM to get twice the torque at 3500 RPM. Does that attempt at explaining make any sense to you?

SJ Foster, please see my reply to gfgdc regarding what Power is vs Torque.

I think you answered your own question: "given the gear ratios and torque curve" - power calc + gears do just that!

A further reflection: the area under a torque-rpm curve (i.e. Integral (Torque) d (rpm)) represents a power quantity (instantaneous power = torque x rpm). Power, the rate at which work is done (or energy is expended, depending on context), will increase the car's kinetic energy on horizontal ground (i.e. speed, given constant mass) as well as overcoming the various drag/friction forces. Hence the area under a torque-rpm curve should be an indication of acceleration across a particular rev range. The complication is that it's not just a matter of using the single engine torque curve like it was for the power curve calculations because the gearing changes the torque available to the wheels for acceleration. Hence I think there will be 6 different torque graphs to integrate and optimise for a 6-speed gearbox. I might try the calculations but will probably just shift according to feel and mood! Trying to do a mathematical analysis involves too many assumptions anyway, no matter whether based on power or torque, such as a horizontal road, neglecting speed-dependent transmission losses, air resistance, etc etc. As one well-known (in academic circles) paper on heat losses from chickens stated in its introduction, "Consider a spherical chicken."

Shift when you want, lol. this is a way to understand what is somewhat mysterious to me. The part I'm not totally comprehending is the "area under the curve" vs the "equal power" method. my intuition is the area under the curve makes sense, and yes you correctly state that its an integral to calculate it. Thinking about it now, the area under the curve has to be right... -- imagine a power curve that spikes after the "crossover point" and one that is a flat line. one has to be better, than the other. Anyway, not to belabor the point. There is an engineering analysis, but no one has to use it! AND, this has no relevance to having fun and tooling around in the car. It us optimization, IF you want to optimize.

This is great work but the more I read about it the less I understand I'm going to have to stay after school I guess that's why I got a PDK after 8 manual Porsches