Power droop
In my original post, I showed the plot below of the battery power and speed as a function of time both before and after the ludicrous upgrade.
It was a mystery to me why the power peaks at about 4 seconds and then gradually drops and then drops even more rapidly after about 8 seconds. I think I now understand this and it is related to whether there is a finite amount of surge power available. Now, I'm not a battery expert and not at all sure about this, so let me lead you through the thought process that lead to the conclusion.
First hypothesis: Tesla's firmware is purposely reducing the power to the motor to keep something (inverter or motor or battery) from overheating. I doubt this is the case, because even before the upgrade the power droops, so if it was a heat problem, there would be more heating (because of more power) after the upgrade and it would droop faster. Also, 10 seconds is a pretty short time period for a liquid cooled system to significantly change temperature. Typical time constants are minutes.
Second hypothesis: Because of back EMF, a higher voltage is needed to drive current through the motor and there is a maximum voltage the inverter can put out. Again, I doubt this since the droop exists before the upgrade.
Third hypothesis: Tesla is firmware limiting the battery current to protect the fuse and contactors and they increased that limit with the upgrade. Given that the upgrade involved a smart fuse so they could run closer to the fuse limit and higher current contactors, this is very likely. The second part of this hypothesis is that they are applying that maximum current the whole time of my acceleration runs. If that is the case, then the voltage from the battery must be drooping during the acceleration run.
I looked into why that could be. It is a fact that lithium ion polymer batteries used for RC airplanes have both a continuous and pulsed maximum discharge rate. The batteries I have looked at allow a pulsed discharge 50% higher than continuous and allow it for 10 seconds. I had no idea why this was the case, but perhaps it is related to the power droop. So, I googled it and found this paper:
https://www.unibw.de/rz/dokumente/getFILE?fid=8968652&fd=kein titled "Utilization of the Battery Recovery Effect in Hybrid and Electric Vehicle Applications" which talks about pulsed power from batteries. In particular, it has a plot shown below of the battery voltage as a function of time when a pulse of power is taken out.
At time -20 seconds in the plot they start drawing a large current. There is an immediate drop in voltage due to the internal resistance of the battery. There is then a more gradual drop in voltage for the next 20 seconds until they quit drawing the large current at time=0. So, according to this plot, the battery voltage does droop when one draws a large current and the timescale is similar to what is seen in my acceleration tests.
The paper goes on to explain the mechanism behind the voltage droop has to do with diffusion of ions through the electrolyte.
Conclusion: In a long acceleration run the power gets reduced over time due to battery physics. So, as lolachampcar suspected, there is a finite "surge" of power available. My test to see if this was the case was to compare the times to go from 30 to 60 mph when starting from 0 and starting from 29. They were virtually identical so I concluded there was no surge. I also compared the times to go from 60-90 when starting from 0 and starting from 59. Again, no significant difference. However, if you look at the first plot, there is only significant droop starting at about 80 seconds and by that time the car is going 80 mph. So, I suspect that if one compared the times to go from 90-120 mph starting from 0 and starting from 89 that the later would be faster. Perhaps someone with access to the German autobahn will test this. I certainly won't be doing so.:smile: For the way most of us normally drive, this droop has no significant effect. For those trying to understand the quarter mile times, it is the reason the hp is slightly reduced in the last part of the quarter mile run.