Coast and Burn (Pulse and Glide) Calculator

Hi all,

So my brother and I are from Perth, Western Australia and we have been building electric endurance vehicles in our garage since 2009 when I was 15 and he was 11. We've now built Australia's most efficient manned land electric vehicle, which achieved 131.7 km/kWh (on a very windy day) and although we're not eligible for the Shell EcoMarathon competition (as we're not an educational institution) we're currently trying to beat the Australasian record of 434 km/kWh.

To try and improve our vehicle's efficiency we're not only improving the vehicle's components but trying to develop a very efficient strategy for the driving of it. One of the most popular fuel saving strategies used by hyper-milers is Coast and Burn (a.k.a Pulse and Glide) but there is very little information currently about it online so I decided to do my own theoretical research to estimate it's effectiveness.
In the following topic, I'm trying to develop a calculator to determine the effectiveness of a Coast and Burn strategy using an excel spreadsheet which takes the following inputs;
- Crr (co-efficient of rolling resistance)
- Cd (co-efficient of aerodynamics)
- Frontal area of the vehicle (m2)
- Mass
- Burn Speed (what speed do you accelerate to?)
- Coast Speed (what speed will you coast down to?)
- Motor Power

and then provide the user with the following information:
- How far will you coast?
- How long will you coast for?
- How far will you burn (pulse) for?
- How long will you burn for?
- Percentage of time spent burning/ percentage of time spent coasting
- wH/km for Burn/Coast Strategy
- wH/km for Constant Speed Strategy

tl;dr Here is the calculator in excel.
View attachment Coast and Burn Calc.xlsx

Time to go back to my Year 12 Physics....

So after a few hours of work, I've come up with the following calculator on excel which I'll explain in this post. I have a feeling that I've forgotten something because although the results make sense with an electric vehicle (given the high efficiency of electric motors), it's saying that it's more beneficial to keep a constant speed in a car than Coast and Burn. If anyone can spot issues with my formulae or general logic in tackling this please comment and let me know.

Here is the explanation of the Coast Phase calculations:



Calculating the Coast Phase Time:
My first step in determining the length of time spent coasting was calculating the average Aerodynamic and Frictional Drag forces acting against the vehicle.
To do this I used the formula, F = Cd.1/2.P.V^2.A, where Cd = Coefficient of drag, P = air density, V^2 = velocity squared and A = frontal area (m2) to calculate the Aerodynamic drag at the Pulse Velocity (max speed) and at the Minimum Speed. I added them together and divided by 2 to get the average Aero. Force. in the case above, it's 7.22 Newtons (N).

I also did this with Frictional force which has the equation F = Crr.m.g, where Crr = Coefficient of Rolling Resistance, m = Mass of vehicle and g = gravity (9.8ms-2), due to all these values being constant regardless of speed, the Frictional Force is constant for a given mass and Crr. In the case shown above, it's 5.886 Newtons.

Following this, I was able to work out the average deceleration rate of the vehicle using a re-arrangement of the formula F = m.a, a = F/m. Therefore the deceleration rate in the above case is 7.22 N + 5.886 N divided by the mass (120 kg) = 13.106 N/120 kg = - 0.1092 ms-2.

The final step to calculate the coast time is to use the equation t = (u - v)/a, where t (time) is = initial velocity (max. velocity) subtract Final velocity (min. speed) divided by the acceleration rate (- 0.1092).

Therefore time spent coasting in above example = (12.5 ms-1 - 9.72 ms-1)/-0.1092 ms-2 = 25.42 seconds.

Calculating Coast Phase Distance Covered and Average Speed:
Now that we now the time spent coasting, it is rather easy to calculate the distance covered as we are assuming an average deceleration rate.
Due to this we can use the formula s = ut + 1/2at^2, where s = distant, u = initial velocity, t = coast time, a = acceleration rate (-ve), t^2 = coast time squared. Inputting the numbers from the above example in the picture we get; s = 12.5.(25.42) + 1/2 (-0.1092).(25.42^2) = 282.55 metres.

To calculate the average speed during the coast phase, I took the distance achieved (282.55 metres) and divided it by the coast time (25.42 seconds) to obtain the average velocity (11.11 m/s). Multiplying this by 3.6 gives the average speed in kilometres per hour, which is 40 km/h.

I'm not exactly sure if you are asking a question in this thread, but....

On a quick glance, it appears that you may be compromising your results by using a simple mean average in the initial steps of your calculation. This is essentially saying that the underlying behavior is linear when we know that it has a large V^2 component. The arithmetic mean uses the endpoints of the curve and ignores everything going on in between...

There are other ways to attack this, but you might simply revise your existing calculations to perform a piecewise linear approximation where your existing calculations becomes a row in a table. Here you divide the min/max speed range into a bunch of separate slices, say into 1.0 or 0.5mph slices using an Excel table. Then perform your calculations across each slice individually to determine the time to decelerate across the slice to the lower speed. You can drag the formula cells or use array formulas to achieve this. This will get you a result where each little section of the speed/force curve is addressed as a short straight line (using your existing arithmetic mean technique) to better fit the curve in place of one big end-to-end straight line (the effect of your present single mean average). Sum up the results from decelerating across all the individual speed slices to get the total time, distance, etc.

Just a thought...

Teklektik, thank you for the advice.
I guess I didn't really make it a question but your response and advice is the exact reason I'm posting the calculator and the process used to achieve it's results on here. I'm not brilliant with maths but see massive value in being able to calculate the effectiveness of the Burn/Coast method and to determine at what speeds it is most effective without manually doing the equations a million times.

I took your advice and processed the quadratic equation in 0.1 m/s slices and got the following results:

Average Aerodynamic Force: 7.13 Newtons instead of 7.22 N
Deceleration Rate: -0.10852 ms-2 instead of -0.109235 ms-2
Time Spent Coasting: 26.902 seconds instead of 25.492 s
Distance Coasted: 295.427 metres instead of 282.54 metres
Average Speed: 39.532 kph instead of 40 kph.

Here is a screenshot of the Excel Spreadsheet:


And here is the actual spreadsheet if you want to see the equations in each line and check my working... I'd appreciate it.
View attachment Coast Phase Quadratic.xlsx

Anyways, I think that the original method is kind of close enough but I will work on two spreadsheets. One that can easily be used for estimations and another for more exact results.

Thanks again for the help

CoulombMotorsport said:

I think that the original method is kind of close enough but I will work on two spreadsheets. One that can easily be used for estimations and another for more exact results.

Click to expand...

The difference between the two methods will be governed by the min and max speed range. For two low speeds, there is little curvature and the end-to-end approximation is not bad. It deteriorates rapidly, however, when you consider larger speed differentials (more curvature between endpoints) and high max speed (increased aero drag). The reason to maintain the version with the poorer estimate is unclear, but whatever works. (If you are concerned about finagling the table each time, that's just a matter of working a bit on your Excel skills so the table population happens automagically - possibly on another sheet. Both versions should be equally easy to use...)

Quickly eyeballing your new spread, I see two things:

• You are not finding the mean speed for each row and are instead using the higher speed alone. It may seem a small thing, but using the mean between each row and the next better implements the linear approximation strategy. That said, what you have is a workable approximation - just not the technique discussed.
• You appear to have omitted the velocity factor from the rolling resistance term. This is easily seen by the constant frictional drag at all speeds.

I didn't really look at the whole thing in detail, but the general approximation implementation looks okay - just needs a little tinkering.

This guy is a retired Ford engineer.

http://www.hyperrocket.com/

He competed in the 2013 Ohio Vetter Challenge.

http://craigvetter.com/pages/2013-Challenges/2013-Vintage-Days-Challenge.html

He says coast and burn doesn't work.

Only got a bit of time to write more on the calculator so I'll write about the easiest part which is Calculating Constant Speed Strategy Energy Usage:

Calculating Power needed to maintain constant speed:

Very similar to the equations above regarding Force needed to overcome Frictional Drag and Aerodynamic Drag, the following equations are power required to overcome Aero. Drag and Frictional Drag:

P = Cd.1/2.P.V^3.A, where Cd = co-efficient of drag, 1/2 P = half of Air density, V^3 = velocity cubed and A = frontal area.
To make the power usage a fair comparison with the Burn/Coast strategy, the velocity used for the above equation is equal to the average velocity of the burn/coast strategy. In the case of the photo above, the average velocity is 11.11 m/s (40 kph).
Therefore Power required to overcome Aero. drag = 0.24*1/2*(1.2)*((11.11)^3*)*0.4 = 78.98 Watts.

Power Required to overcome Frictional Drag is = Crr.m.g.V, where Crr is co-efficient of rolling resistance, m = mass, g = gravity constant of 9.8 ms-2, and V = velocity (11.11 m/s). Therefore Power required to over Frictional Drag = 0.005.120.(9.8).(11.11) = 65.32 Watts.

Hence, total power required is 78.98 Watts + 65.32 Watts = 144.3 Watts.
However, you'll see in the above photo that Power Used = 167.50 Watts. This is because the motor efficiency at constant speed = 85%, so the power actually required is equal to 144.3 Watts*(1+(100-85)/100)) = 167.5 Watts.

Thus maintaining a speed of 40 kph, you'll use 167.5 Watts constantly. Therefore, you'll use 167.5 wH to achieve 40 kilometres, which is equal to 4.1875 wH/km.

Thanks Teklektik, I'll fix that.
Also, I only just realised I omitted velocity from the power calculation for rolling resistance in the Constant Speed section. Makes a big difference.
Note, velocity is omitted in the Frictional Drag section for the coasting because it's the Force in Newtons not the Power in Watts. The velocity component is only added when converting that force to a power as it adds the dimensions of time and distance.

Work (Joules) = Force x Distance
Power = Joules * Time

I'm sorry for all the mistakes, I'm trying to find and fix them all. It's quite a challenge actually with all the variables etc.

If you'd like, throw some of the equations at me and i'll stick them in java and build a quick GUI in it (Like https://goo.gl/23d62r)
Looks like a pretty neeto setup you've got. If someone had mentioned it to me, i'd call them crazy saying pulse and glide would be more efficient than straight cruising.

Pulse and glide is a strategy that works on hybrid cars where the thresholds of background regen and acceleration power from the electric motor are not easily variable.

For example, on my 2000 honda insight, the background regen will provide 3 bars ( out of 15? ) and no more.. and there's a certain throttle position that turns on, and a certain throttle position that prevents it from happening. Same with the electric assist. There are only 3 levels of electric boost, really. It just turns throttle positions into whatever level of electric assist it thinks is appropriate for the condtions..

So, pulse and glide is a technique to control that better. It is effectively pulse width modulating your hybrid drive system with your foot.

I would imagine that this is not useful on an EV, since the degree of modulation of the power is much more variable.

Pulse and glide is not relevant to EVs imo. The intent is to better utilise portions of the engines volumetric efficiency curve that deliver better energy return from a given quantity of fuel. This is a surprisingly high level of throttle input and rpm on petrol powered engines, so this behavior is not something that can be maintained steady state. The glide is to reduce your average speed sand means more of your fuel is being burnt in an efficient manner overall. This technique isn't limited to hybrids but can work very well on them for all the reasons neptronix mentioned.

For reference search for volumetric efficiency, throttle pumping losses and BSFC.

Electric motors also have an efficiency curve, but it doesn't vary a whole bunch.

Hi everyone,

Firstly thank you for all the replies and the discussion. I've been traveling the past two days, only just getting home in Western Australia after studying and visiting friends in Europe for the past 4 weeks, and it's nice to get home and see some good discussion. Thanks eTrike for the praise, a lot of work and money has gone into developing our vehicles.

Secondly, the whole reason I started developing this calculator was to try and see whether Coast and Burn worked for EVs especially seeing as some of the best battery powered ECO-Marathon teams use it.

4skeen, thank you very much for the offer. I'm currently doing a big write up and also a Youtube video explaining the calculator and once I'm happy that everyone approves of it I'll send you everything I've got. I suck at Java so that'd be a great help

Hi everyone,

Here it is, a reasonably quick explanation of how I designed the calculator and how it works in the excel sheet.

https://www.youtube.com/watch?v=GQp0u5-NE6I

Also here is the most up to date calculator:

View attachment Coast and Burn Calc.xlsx

Thanks again for all your help so far.

James

When slowly decelerating on super highway mode with a prius 2, it does the same as pulse and glide. What do you think about slowly decelerating instead of gliding?

Hi Hyperion,

Sorry for the very late response, I've been rather busy lately.

In my experience, due to the Prius being an automatic, when you're slowly decelerating in the Prius on the highway you are still actually consuming fuel unless you put it into engine braking mode. I.e. if the energy required to overcome air resistance requires 40 HP* and the engine is only outputting 35 HP** you will be slowly decelerating while still burning fuel. Therefore slowly decelerating doesn't give the same effect as gliding where the motor is being driven by the wheels and doesn't inject any fuel.
* & ** made up numbers for example.

Whilst in the US, I achieved 58 mpg in a Prius by accelerating gently from a stop, maintaining a constant speed on the highway except where there were hills in which case I eased off the throttle to maintain fuel burn rate (mpg) on the climb, and then sped up a little on the way down using the battery. Approaching lights and intersections I used engine braking wherever possible and recharged the battery. This all helped raise the MPG considerably. Over at Ecomodder.com, there are people who coast and burn and get better MPG with their Prius' but I think that 58 mpg was good given I didn't hold up traffic at all (moved to the right lane when approaching hills) and I also had a decent average speed of 70 mph.