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iisjsmith said:So we can assume that as the Roadster accelerates from 0 to 80mph (0 to 8000rpm) the inverter is slowly increasing the frequency and voltage supplied to the motor. It increases the frequency to increase the motor speed, and increases the voltage to keep the volts/hertz ratio constant.
Now once we hit 80mph the motor is spinning at 8000rpm and we are at maximum power. As we accelerate past 80mph the inverter continues to increase the frequency supplied to the motor...but the voltage no longer increases. The volts/hertz ratio starts to change from the baseline and our available torque starts to suffer. But since the voltage is not increasing we are not draining the battery pack any faster.
So the range for the Roadster should be no different if you are going 80mph or 130mph. Driving slower than 80mph will increase your range.
okashira said:WarpedOne: I'm going to throw your some ideas/thoughts to try and help improve your calcs:
1.) you didn't include motor effiency in any of your estimations. Just use 90% across the board. this will lower your range calcs.
--I.E. 0.9*power sucked from battery = power put out by motor(250 peak)
2.) you estimate at top speed, 135 that the motor is producing peak HP at that rpm (max rpm) when in fact the top speed is gear limited and the car is still accelerating when it hits redline at 135mph. so infact to travel 135mph it needs LESS then the peak hp at 13500 rpm (or whatever peak rpm is, dont feel like looking it up) try assuming it uses 80-90% of that power. this will increase your range calcs.
3.) I think that going to a power reqrment that's a cube of the speed at such a low speed is a bit much. say perhaps it doesnt become a cube until 80+mph. then scale evenly.
iisjsmith said:I am in no way an EE. But I have spent several weeks researching PWM and other VFD technologies for a pet project of mine, and I finally understand how they work.
You can spout equations all day long but it doesn't change that fact that at some point you are only increasing the frequency of the power, not the voltage. You cannot supply a voltage greater than the line voltage, which in this case is a nominal 375V. I believe I calculated that the frequency of the power at 8000rpm would be 266Hz. I admit I don't remember the reference...I'll have to check my links.
So once you are supplying the inverter with 375V at 266Hz you are at the max of the volts/hertz curve. Anything above that means only increasing frequency, which does not consume more power. So while drag might increase because you are going faster, you do NOT draw more power from the battery pack.
This is just the way PWM inverters work.
in order to get the desired power, the computer/inverter/whatever varies the voltage based off 'throttle' position.
iisjsmith said:in order to get the desired power, the computer/inverter/whatever varies the voltage based off 'throttle' position.
I'm sorry, but you should really read my previous posts again. This is not a potentiometer system, like those found in DC motor systems. The throttle does not vary the voltage to the motor, thus altering its speed. The throttle position tells the inverter what frequency to make the electric power that is fed to the motor. The voltage adjustment is made by the inverter, and that has nothing to do with speed...only torque.
this is not really a discussion about electric cars, ICE cars or whatever. it's just about the driving range of this particular vehicle.There are some very helpful online resources for explaining the way pulse width modulation inverters work in relation to AC motors. The one I like the best is the Siemens website...they have some online courses at http://www.sea.siemens.com/step/default.html. If you just want to download the PDFs you can go to http://www.sea.siemens.com/step/downloads.html. Focus on the sections titled "Field Weakening" and "Volts per Hertz". They explain how the voltage is adjusted.
Saying that electronics and inverters have no place in this discussion is like saying carburetors and fuel injection systems have no place in a discussion about ICE vehicles.
The throttle absolutly does not control frequency. the frequency is dependent on the motor's speed, NOT the other way around.
it does infact control torque (via voltage to the motor.)
Instead of reading more about ac motors, you should pick a physics book.iisjsmith said:ac stuff
Ill leave you with this: at 80mph, it only takes about 40-50 horsepower to keep the car in motion (probably even less for the tesla). if your car is puttering along at 80mph, and the motor is producing 250hp, where is all that leftover energy going? (serious question)So you cannot discuss range of the Tesla Roadster without factoring in the way their drive system works. And I stand by my opinion that you will see a maximum battery drain at maximum power (80mph) and then NO additional battery drain as you go faster.
iisjsmith said:I'm sorry, but this is completely incorrect. Any basic....[removed indignant text] AC motor theory and you will see that the speed of the motor is controlled by only two factors: the number of poles and the frequency of the power... the frequency can be adjusted by using an inverter.The throttle absolutly does not control frequency. the frequency is dependent on the motor's speed, NOT the other way around.
Again, this is completely incorrect. In a potentiometer system you would be right... This is NOT how the Tesla Roadster and other AC motor drive systems work. It uses a variable frequency drive system to alter the frequency of the power.it does infact control torque (via voltage to the motor.)
So you cannot discuss range of the Tesla Roadster without factoring in the way their drive system works. And I stand by my opinion that you will see a maximum battery drain at maximum power (80mph) and then NO additional battery drain as you go faster.
cor_van_de_water said:Note that although I am an EE, I have not majored in power electronics or motor technology, it is mainly from practical experience and reading up on AC drive that I came to the above understanding. Please correct any errors or omissions.
BTW - In practice, I use my AC drive all the time, because my truck has an AC drive alike (but of lower power) than the Tesla.
You can see it here: http://evalbum.com/694
To JoeG:
1. Classic ICE car spends driving energy into 3 major losses.
1.1 Rolling resistance
1.2 Airodynamic drag
1.3 Acceleration of a car
2. Rolling resistance produces approximately independent of velocity drag force proportional to actual car weight. For passenger car for estimation we could assume it fixed around ~200 N ( weight of 45 pounds approximately ). You could feel it for yourself by putting passenger car to neutral gear and pushing it from stop on an even surface.
3. Airodynamic drag force is approximately prorortional to square of velocity. It is characterized by Cd coeeficient of airodynamic drag. For most of cars except very airodynamically efficient the airodynamic drag would become roughly equal to rolling drag at velocity of 50 mph. So for 25 mph it would be 1/4 of rolling drag and could be neglected. For 80 mph freeway driving very common on real roads airodynamic drag would be 2.5 times higher than rolling drag force coming up to ~500 N ( weight of 110 pounds roughly )
4. Acceleration of the car energy loss channel comes from the fact of increasing kinetic energy while accelerating and losing all these energy into heat in brakes while braking. It is very roughly proportional to square of your final velocity and to number of accelerate/brake cycles per each hour on average you doing while driving. It is also proportional to actual mass of the vehicle while driving.
5. There are numerous less influencial factors like variations of engine efficiensy with engine load changes, losses related to hills climbing, losses related to engine heating at start up etc etc. Overall picture is very complicated but for basic understanding mentioned 3 factors are major one to get an idea.
6. Freeway driving because of higher average speeds dramatically increases 1.2 component. But on a freeway you could let car “free” rolling in case if you need to reduce speed and avoid using brakes heavily. This would dramatically reduce 1.3 factor. Reduction in 1.3 typically dominates over increase of 1.2 so you get higher mpg for freeway driving.
7. Hybrid cars and full electric cars are recovering 50 % to 90 % of otherwise wasted energy for 1.3 component. This is done using what is called regenerative braking. Electric drivetrain is critical for this ability. As a result for good hybrid car city driving (lot of start/stops but lower average speed) become significantly higher mpg than freeway driving. In short hybrid car gives you very good handling and efficiensy in case if your typical traffic pattern involves many start/stops. For freeway driving some efficiensy boost exist but much smaller.
8. Because of the regenerative braking percepted by driver fuel efficiensy of hybrid or electric car has a property to reduce very fast with increasing speed. In classic ICE car the effect is mostly masked out by much lower efficiensy of ICE engine at lower speeds. This is not true for electric motors hence perceived high efficiensy boost for low speed driving and city driving with hybrid and full electric cars.
9. Aside from the issue of battery cost and battery depreciation cost in terms of energy use full electric car is more efficient than hybrid. The difference is that full electric car gets electricity generated by centralized electricity generator with efficiensy 50 % to 60 % of fuel energy coming into electricity. Hybrid car electricity is generated locally in the car. Under such portable conditions efficiensy of transforming fuel energy into electrical (or direct driving mechanical energy for that matter of classic ICE car) would be 25% to 30%. This factor manages claimed twice efficiensy advantage of Tesla roadster versus Toyota Prius.
10. It is very difficult if possible at all to match the energy efficiensy of centralized electrical generators by car ICE engine. The fundamental reason is that high pressure turbines with combined gas followed by steam cycle have fundamantal efficiensy advantage over ICE. But they are inherently bulky, heavy and require very qualified (expencive per unit) maintenance. So portable mass serviced ICE engines are inherently inferior with energy efficiensy. That argument answers to whoever say full electric engine should have the same efficiensy as ICE considering primary energy source like oil.
11. Unfotunately today battery cost is still too high for normal car market price range. If battery cost and battery depreciation cost for Li-ion batteries is included into ownership cost it makes driving more expensive per mile for full electric car versus hybrid and classic ICE cars. This factor explains why full electric cars are not dominating car market today and will not most likely come to below $30000 car price range over next 5 to 10 years at least.
But if very common SLA lead acid batteries cost is considered per unit of energy ownership cost of full electric car becomes competitive versus classic ICE cars or hybrid cars. Unfortunately these batteries do not fit power density and energy density requirements of cars well enough. But this story gives hope that with time Li-ion batteries would drop in cost 4 to 5 times. If and when this happens full electric cars would very rapidly come to mainstream and replace sizable percent of total car fleet.
12. It is also very clear that by reducing car total weight one could enhance its mpg very greatly. This is the main factor of extremely high energy efficiensy of super-light cars and bicycles.
To JoeG:
Forget to answer about Tesla roadster mileage versus speed. Using data from the blog and Tesla site I once managed a simple Excel model for this. Because I am “random blogger” you should take my data with a grain of salt. They surely are not very reliable and Tesla Motors people could easily dismiss my numbers. Unfortunately to me personally they are not so great looking for Tesla Motors promotion but anyway I belive in my model enough so denying these numbers to me would require poof. Anybody else could choose what to believe.
My model data are as follows:
1. Maximum range is 370 miles but at velocity in 20 mph to 30 mph range.
2. Claimed 250 miles range comes for velocity around 50 mph.
3. At sustained velocity 65 mph range comes down to 190 miles
4. At sustained velocity 80 mph range reduces to 140 miles
5. At sustained velocity 130 mph range would be 60 miles (some race track ride I guess)
So apparently Tesla roadster is not a match for racing car. It is not very fit for people in love with power, engine sound, smell etc and outrageous speed on a race track (or illegally on a road). But Tesla roadster is extremely good fit for heavy traffic road with the need to fill gaps very fast. It would be also very pleasant low noise scenic drive for curly countryside roads (along the Pacific coast for example) with numerous of acceleration/braking cycles but average speed below 50 mph because of curves and speed limits.
I guess Tesla Motors have good enough sales already so they are not promoting their car in public using very specific and honest account of advantages and disadvanatages agains other rides available. They obviously do it individually for their customers as I noticed from customer blog posts.
To Dean :
Range data via the reference you provided are based on interpolation models ( linear, square, cube ) with fairly arbitrary points to switch between interpolations. This is fairly far from how car uses energy. My model used forces and power considerations as follows:
1. Airodynamic efficiensy Cd = 0.39 (indicated by Martin Eberhard in one of early blog posts). Frontal area was calculated from Tesla roadster dimensions from the site.
2. Rolling resistance was calculated based on car weight from the site with rolling resistance factor of 0.015 (pretty typical for normal tires). This value also matched against claimed EPA mileage of 250 miles so I assumed it is close to reality.
3. I assumed useful driving energy for battery pack of 52.2 kWh using many data points from the site. Using battery capacity I get the idea that all the batteries correspond to 2C discharge making up sustained power 52.2 x 2 = 105 kW. This also matched torque/power curves from the site and based on resistance data from 1 and 2 it matched 130 mph top speed.
4. I assumed fixed 1 kW power for air conditioner etc appliances. This number is most arbitrary but it influences only fraction of range decrease at very low speed of 5 mph, 10 mph etc. The main effect is that range maximum shifts to 20 - 30 mph area as I think it would be in real life.
Altogether you get sum of power factors like: = A + B x + C x ^ 3
This is the simplified model of having fixed in car power factor A, rolling resistance losses factor B and airodynamic drag factor C. Major influence factor C is fixed by data from the site. These factor work together so instead of arbitrary interpolation far from physics you have oversimlified but physically correct picture based on actual forces factors. Engine efficiensy is fairly flat and accounted inside A, B, C values. Assumed value was 90%.
Such a model get range data with about 20% to 30% accuracy I think. This approximately matches the accuracy of input parameters I have used. Getting better precision is pointless because you start having specific for each car specimen, trip peculiarities, road peculiarities etc results. Car improvement evolution before production expected would also most likely fit under indicated 30% uncertainty. I would not be much sirprised if actual data from real car would be even slightly worse than my numbers at least above 80 mph.
I used model based on car energy disspation physics with just 2 adjustable parameters (A and B above). I used few data points (250 mile range EPA, 200 miles range for sort of highway driving, 130 mph top speed, 52 kWh per 6831 18650 batteries match against market, 0.4 MJ / km energy dissipation of Tesla roadster, 110 mpg efficiensy claim etc) to match adjustable parameters. Everything I learned from Tesla Motors site matched within 5% accuracy into my model with same single set of parameters in realistic range. So I assume that my data are more close to reality versus pure speculative interpolation model. But none of us has any definite proof and so far Tesla Motors people were reluctant to say anything much about range variations with speed. Because I am not the customer I have no rights to demand any data or insist on my conclusions. My numbers are my pure speculations made just for fun of scientific style investigation (my former scientist habits).
Once the EPs were built, they were put to the test. It’s a hard life when testing involves driving a performance car, but someone has to do it. The PEM team was convinced that they could get more power from the PEM. This would result in more power to the motor, which would deliver more torque, thus improving the acceleration. Phew.
They moved around the Insulated Gate Bipolar Transistors (IGBTs) in the motor power driver to make room for 12 more. The increase in torque was noticeable. The result was a quicker 0-60 time – it shaved off about 3/10 second. You can see the increase in torque from the additional IGBTs in the Fast Torque graph. (Click on the graph to enlarge it.) It shows an increase of about 25% in the middle of the RPM range. Nice.