I’ve put together few charts that illustrate the point that I’ve been making for some time: that the improvement in 0-60mph acceleration that Tesla was able to achieve in P85D vs P85/85D (0.8 sec), in spite of the power limitation imposed by the battery, is mostly due to the increased combined torque available from the two motors with more that 50% increased power rating (686lb-ft in P85D vs. 443 lb-ft in P85).
First, few basics. As I mentioned before, based on the Second Newtown Law, acceleration is defined by the applied force. As applied to the rotational motion, the acceleration *time* is defined by the applied torque and is proportional to total connected inertia and reciprocal to the accelerating torque (the difference between the torque of the motor and the load torque). For those interested in more details, they are available from the “
Calculating Motor Start Time” on-line course. The pertinent formula illustrating the above statement is included below.
As I’ve mentioned many times before, based on the above, the accurate estimate of acceleration can be performed only by analyzing the torque and power curves, not by comparing a single point from these curves across technologically different drivetrains which yield very different torque and power curves.
Here is how the idea of acceleration being accurately ascertained using the torque curve was expressed by the former Mazda Engineer that worked on Miata Project in his book (Norman H.Garrett III, Mazda Miata Performance Handbook):
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So, I started with building the power curves for the P85 and P85D, based on description that I’ve provided
here. The curves are based on current specification of the P85D (728hp), because I did not have access to the rpm values that correspond to the older (691hp) specification. The curves are idealized, i.e. do not take into account transients and decrease in power output of the motors at higher speeds, as I do not have the necessary data to accurately represent these effects.
The combined power curves for P85 and P85D are shown using shading – the green area outlines P85 curve, while green plus yellow area outline the P85D power curve. There are two charts – one using rpm on the horizontal axis, another – mph. The mph are calculated based on 9.73:1 ratio (common for both front and rear motors per the Model S Manual) and based on the tirerack data for the 245/35R21 Continental DW summer tires (750 revolutions per mile).
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The torque curves are built based on the power curves, taking into account that the drivetrain outputs rated torque (horizontal portion of the torque curve) up to the speed at which it reaches its power limit. After this inflection point the torque declines with the increase of rotational speed (rpm) so that power limit is not exceeded. The torque curves are built neglecting the transients and the fact that the power limitation imposed by the battery is not a horizontal line, but a line that is sloping down with the increase in rpm.
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As seen from the attached charts, the increase of the area under the torque curves from 0-60mph (which is proportional to power) can be divided into three areas. Area A represents improvement in acceleration due to the increased combined torque of P85D over the P85 (686lb-ft vs.443lb-ft). Area B represents improvement due to the increase in power limit of the battery from 416hp to 463hp. Area C represents improvement in acceleration due to both motor torque and battery limit improvements.
I will do actual calculations next week, but as can be seen from the graphical presentation, splitting area C in half, with each half allocated to the improved acceleration due to torque and horsepower improvement, it is clear that (0-60mph) acceleration improvement due to the increase in combined rating of the drivetrain motors dwarfs improvement due to increased power from the battery. Just eye balling it for now, I would say that 85-90% is due to the increased drivetrain motors, while 10-15% is due to increase in battery power.
In summary, your conclusions are not consistent with the data and are simply wrong.
The analysis of these curves, as I alluded before, leads to several additional implications, including the one that I repeatedly referred to by saying that square peg does not fit into the round hole, and I am sure that the lively discussion on this topic (as it is central to the assertion made in the unhappy owner’s letter) is next…