I was wondering if anyone has considered how to calculate optimal acceleration for an electrathon vehicle?
For the past couple of months, I have been tossing around ideas for how to calculate the optimal rate of acceleration when coming out of corners. For some reason I get confused every time I weight the rule of thumb about accelerating slowing to save fuel against the value of accelerating quickly to get up to optimal speed.
I used this formula in my engineering class now this is THEROERTICAL, in real racing these numbers will be higher due to drag, friction, motor power loss, etc
Just for those who don't know all the weird symbols for stuff
I = amps
m = mass
Vi = Velocity Initial (Speed at end of the turn)
Vf = Velocity Final (Target speed at straightaway)
t = Time (seconds)
V = voltage
V = Vf - Vi
g = gravity (32.1 m/s^2
The formula is as follows
I = ((w/g) x (V^2)) / 2Vt
Now for you that last part is what you need everything else is constant so add speeds you need, car weight (with you and batteries) and voltage (this is where higher voltage is more efficient)
With this you can weigh the positives and negative for acceleration speed but also determine track size, you its a long straight a way then faster acceleration might help since you can be a optimal speed for so long but on small track where corning speed is not much lower then straightaway speed you might want to go slower since you are so close to optimal and it would waste power accelerating faster.
If you need that formula in a simpler form (How it would be handwritten) or an example feel free to ask.
You can also use this with starting line acceleration just change V with Vf, since Vi is 0
Do you have any thoughts on how to calculate optimal acceleration for electrathon?
By way of example I am trying to think through the following test.
Objective: Starting from stand still, go as far as possible in 1 minute down a straight and level course in an electrathon vehicle with a battery capacity of 500 Watt-minutes.
It is very easy to calculate the optimal steady state speed over the course by determining through testing how fast the vehicle can go while consuming 500 watts per minute. My questions is how should we accelerate to go from a stand still to our optimal speed to go as far a possible.?
Do we?
A. Set the throttle for 500 watts per minute and slowly accelerate for the duration of the test? or
B. Accelerate as quickly as possible to bring our vehicle up to an optimal speed? In this test we might consume 50 Watts in the first 5 seconds leaving 450 watt for the remaining 55 seconds. Thus our top end optimal speed is slightly less than with test A, but we do spend more time at that optimal speed.
C. Accelerate somewhere in between those extremes.
My apologies if this is a strange question, I spent 16 hours in my prius last week on a road trip. I spent a lot of time playing with the resume feature on the cruise control in eco, normal, and power mode to see how quickly we got back up to speed:)
Well it seems you know what to do and acceleration speed will matter the track. If you were to do that test on a drag strip if I were you I would invest in a high end power analyzer (link at bottom), I found this one that I want to put on my car its $50 and has 8 things it calculates. I don't have this part yet but when I do I will tell you how it goes. But it could measure the watt hours then by doing difference acceleration during your testing time you can find out how fast you can accelerate for your track. But lets say you are on a quarter mile track such as one at a school then you can have some practice, if you accelerate fast you will draw more power but you will be at optimal speed longer but will it be worth it? if the straightaway was 200 yards sure. But there is no perfect formula to calculate it, only theoretical, unless you want to do some deep analysis of your car. So get a nice meters and electrical gadgets for and test acceleration during practice time. Or if you only have 1 set of batteries or unable to charge and have 2 sets you could go to a empty road and do some test at say 50, 100, 200, and 500 yards and accelerate slowly and then go faster each time at each distance. Then you can find if the average amps pulled in that short distance is higher or lower at faster or slower acceleration. Then you go to the next distance and do more test finding amps. Then use that info on difference tracks even with irregular straightaways. If you spent enough time you could make a amp/acceleration graph for each distance. If you put distance on the X and average amps on the Y and have 3 lines one for slow, medium, and fast acceleration. I made one all these numbers are made up but the curve is what I think would happen at a magic distance where acceleration would not matter. So if you were to do testing you could set it up like this and just have a copy in your car and garage
Blue line is slow acceleration
Orange is medium acceleration
Gray is fast acceleration
http://www.powerwerx.com/digital-meters/dc-inline-watt-meter-power-analyzer-powerpoles.html Power meter site
I agree with the testing bit. I am currently working on an arduino based programmable cruise control for my vehicle :)
Using sensors similar to the one you describe and an output to the motor controller (throttle) a driver should be able to run the tests you describe until they find the sweet spot for efficient acceleration.
I was curious if others had looked into this issues and how they decide on their driving style.
I thought this would be a great science fair project to find optimal acceleration, so I did. I tried to find the optimal acceleration for my Electrathon car. Now on a short track (50 feet between sharp turns) I will use 62% more energy if I accelerate as fast as possible vs slowly. On a larger track (300 feet) between sharp turns I use 42% more power to accelerate fast. On a 1/4 track where you go full speed the whole time and you don't have to slow down and you go 20 miles only accelerating you will use 1.55% more power accelerating fast. On the Ford proving grounds 5 mile track if you accelerated as fast as possible vs someone who didn't you would use .27% more power. The distance then between those cars, over 1/4 mile. So if the top cars were to all accelerate as fast as possible they would travel over 1/4 more with only .27% more power!
I did do this testing by accelerating to top speed and write down the time to get to that speed. For me to get to top speed was 12 seconds in 175 feet, slow was 30 seconds in 300 feet. Then I found how much power I used and did some math and that is how I got all of these numbers. I think this shows how important it is to get a good turning car on slow tight tracks and accelerating fast on a long track can help possibly get an extra lap.