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Thrust Curves
I haven't been overwhelmed with the performance with the new cams so decided to get to the bottom of why it feels the way it does. Back in my sportsbike days I read an article in Performance Bikes about thrust curves which graphs the force that propels the vehicle at the interface of the tyre to the ground. The maths is pretty straight forward but graphing it in Excel isn't. The gist of it comes from the old high school physics formula F=MA, and working in the decimal system F = force in Newtons, M = mass in kg and A = acceleration in meters per second per second (msˉ²). Considering the mass of the car effectively remains constant you can say F is proportional to A so if you can graph F you can see the relative size and shape of the acceleration curves for each gear.
This part is pretty easy to work out by starting with the units we have available. Force is measured in Newtons and Torque is measured in Newton-Meters so if we work out the torque at the tyre and divide by the radius in meters we're left with the Force accelerating the car. The difficult bit is plugging all of this into Excel to graph the Force across the engine's torque curve for each gear. Because we want to use road speed as the x axis so all the gears can be shown on the same graph, the x values need to be calculated, so they aren't in a regular progression like 10,20,30km/h - we end up with x values like 46,50,55,59 and that's why it's difficult because Excel doesn't like uneven spacing on the x axis. I found a way to graph it though but it was a real pain using a time format of all things. To save you all the hassle here's one with the data from my last dyno run with the 265 degree cams - Thrust_Curves.zip You only need to enter data where the cell is yellow but you do need to know the ratio for each gear and your diff. This is an excellent page for data on Toyota's manual gearboxes http://users.tpg.com.au/users/loats/technical/ma61/gearboxes.html. For diff ratios check my Diffs page.
Graphs & Shift Points Here are the thrust curves of each gear with the standard cams in my car.
The calculations are made from 3000-7500 RPM because that's what was on the dyno chart. You can see there's no point revving each gear out as the force drops away significantly and the ideal shift point is where the lines cross. I've added a sheet in the Excel file so you can put in the speed for the shift point and it'll calculate the RPM.
Notice something? The best shift point is different for each gear! I've spoken to Andy about this and he thinks it'll be pretty easy to use the Adaptronic to flash the shift light on at a different RPM point for each gear, as it already calculates which gear is currently selected. If the thrust curves don't intersect (as you'll see below) the best place to shift is at redline.
Comparison with 265 Degree Cams Here are the thrust curves with the 265 degree cams fitted with the same vertical scale as above.
To make it easier to see I've laid the 2 graphs on top of each other. Standard cams are dark and the 265 degree cams are faded.
With the 265 degree cams, the absolute force is lower due to the drop in torque, but it extends further in each gear. On the track only gears 2 and up are used so below 80km/hr the car is slower with the 265 degree cams but after that it should be quicker. What I found in practice is that it because the gearing extended so far (eg changing from 4th to 5th would be at 210 instead of 165) the car constantly felt like it was geared too tall. Maybe I just wasn't used to it but it just didn't feel right. With a shorter diff ratio like a 4.5 the absolute force could be increased and the gear spacing brought back to something more appropriate. However, this would change the character of the car too much for a road car, especially one that gets driven for 10 hours from Sydney to Melbourne so I won't be going down that path. What this really makes obvious is the relationship between the torque curve, the ratios of the gears and the diff ratio. Mess with just one of these and the overall result will probably be out of whack. Now, compare the graphs above to this which is from a supercharged Soarer using an M90 with 10PSI. Blows me out of the water.
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