Hello everyone. One thing that I noticed is that everyone seems to come to the intuitive understanding that the base 35k version of the Model 3 will be a single motor version, but after thinking about it for a little bit I'm not quite so sure.
At first blush it would seem like an AWD model would be significantly more expensive, but when you look at it more closely this may not be the case. Unfortunately I didn't really have to time to do something rigorous, but I think this might be a sketch for an argument for a base AWD version of the model 3.
So first we must realize that the motors, gears, and power electronics will be more expensive for an AWD set up. In general the price of an electric motor scales as the square root of the motors horsepower. So assuming that Tesla is shooting for 250hp we can find he difference in price for the motors.
Assuming two 125hp motors vs. one 250 hp motorPrice ratio = 2*sqrt(125)/sqrt(250)=1.41
So assuming that the 250hp motor cost approx $2k, I have no idea if this is in the right ballpark, the two 125k motors would cost $2828. So we have $828 we need to make up.
However, it is the case that due to always being able to operate the motors at this maximum efficiency point, the AWD configuration is more efficient than the SWD configuration. At first blush this doesn't seem to make much difference as the p85 has a 265 mile range and the p85D has a 270 mile range, not a significant difference. However we have to remember that the p85D is significantly heavier than the p85 lowering the range.
We can therefore perform a calculation to see what the change in efficiency would be in the case that they had the same weight.
Assuming a 4200lb weight for the p85 and a 4400lb weight for the p85D, and that range depends linearly on weight which it generally doesn't.
265 miles *(4200lbs/4400lbs) = 252 miles(270-252) =17/265 ~7% efficiency increase.
Now you ask why even consider the two cars at the same weight as in the real world a dual motor setup will obviously weight more. However, what we must consider is that when tesla is designing the car and the battery pack from scratch they get to choose the capacity they need. So with a higher efficiency they can select a smaller pack.
If we assume that a 50kWh pack is required for their 200 mile target with a 7% increase they would only need 46.5 kWh. If we assume even a very low price for batteries $200/kWh this offsets $700 of the cost of the AWD. Leaving only $128 of the cost left. If we assume a higher cosf batteries as in the 7kWh powerwall it could amount to nearly $1500.
As for offsetting the weight if the powerwall weights 220lbs then 1/2 of that weight is 110lbs so that goes quite a way to the offset.
Summary
The higher efficiency of the AWD configuration could make it less expensive or negligibly more expensive to sell a something like a 46.5kWh Model 3D rather than a 50kWh Model 3.
At first blush it would seem like an AWD model would be significantly more expensive, but when you look at it more closely this may not be the case. Unfortunately I didn't really have to time to do something rigorous, but I think this might be a sketch for an argument for a base AWD version of the model 3.
So first we must realize that the motors, gears, and power electronics will be more expensive for an AWD set up. In general the price of an electric motor scales as the square root of the motors horsepower. So assuming that Tesla is shooting for 250hp we can find he difference in price for the motors.
Assuming two 125hp motors vs. one 250 hp motorPrice ratio = 2*sqrt(125)/sqrt(250)=1.41
So assuming that the 250hp motor cost approx $2k, I have no idea if this is in the right ballpark, the two 125k motors would cost $2828. So we have $828 we need to make up.
However, it is the case that due to always being able to operate the motors at this maximum efficiency point, the AWD configuration is more efficient than the SWD configuration. At first blush this doesn't seem to make much difference as the p85 has a 265 mile range and the p85D has a 270 mile range, not a significant difference. However we have to remember that the p85D is significantly heavier than the p85 lowering the range.
We can therefore perform a calculation to see what the change in efficiency would be in the case that they had the same weight.
Assuming a 4200lb weight for the p85 and a 4400lb weight for the p85D, and that range depends linearly on weight which it generally doesn't.
265 miles *(4200lbs/4400lbs) = 252 miles(270-252) =17/265 ~7% efficiency increase.
Now you ask why even consider the two cars at the same weight as in the real world a dual motor setup will obviously weight more. However, what we must consider is that when tesla is designing the car and the battery pack from scratch they get to choose the capacity they need. So with a higher efficiency they can select a smaller pack.
If we assume that a 50kWh pack is required for their 200 mile target with a 7% increase they would only need 46.5 kWh. If we assume even a very low price for batteries $200/kWh this offsets $700 of the cost of the AWD. Leaving only $128 of the cost left. If we assume a higher cosf batteries as in the 7kWh powerwall it could amount to nearly $1500.
As for offsetting the weight if the powerwall weights 220lbs then 1/2 of that weight is 110lbs so that goes quite a way to the offset.
Summary
The higher efficiency of the AWD configuration could make it less expensive or negligibly more expensive to sell a something like a 46.5kWh Model 3D rather than a 50kWh Model 3.
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