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A power meter can serve a number of useful purposes, depending
on what model you use. Something like the *Cycle Analyst*
can provide a number of useful features in addition to the
simple task of helping you manage your battery pack power
output.

With a little external computation, you can provide yourself with more very useful features:

- Range calculation

The *Cycle
Analyst* can provide an indication of the fuel
economy of you and your vehicle in units of Watt-hours
per mile (Wh/m). You can monitor this value in your
daily rides to determine what is typical for your
situation and vehicle and use that to estimate your
range.

Say you have a 36V 10Ah pack and you only want to discharge it down to 60% of its rated capacity and your typical fuel economy is 20.0 Wh/m.

amp/hr rating x pack voltage x % of pack discharge rating Range = --------------------------------------------------------- fuel economy in watt-hours per mile (Wh/m)

10Ah x 36V x 60% 10.8 miles = ---------------- 20 Wh/m

So 10.8 miles would be your calculated maximum distance at that fuel economy and discharge capacity. 80% discharge would provide a 14.4 mile range but might be harder on your battery packs, and a 36V 20Ah pack at 60% discharge would provide 21.6 miles at this 20 Wh/m fuel economy.

Given your pack capabilities and desired range, determine the required fuel economy. Calculate the required fuel economy to travel 15 miles using a 36V 10Ah pack at 60% discharge:

Required amp/hr rating x pack voltage x % of pack discharge rating Fuel = --------------------------------------------------------- Economy Range

10Ah x 36V x 60% 14.4 Wh/m = ---------------- 15 miles

So your power meter doesn't calculate fuel economy, or you want to know the maximum speed you can sustain to arrive at your destination.

On my recent 104 mile ride, I averaged 13.0 Wh/m at an average speed of 22.3 mph consuming 1345 Wh of energy. I can estimate the required average rate of power consumption in Watts using this formula:

1345 Wh (Battery Capacity) 288 Watts = -------------------------- 104/22.3 (Distance / Speed)

I tried to average around 265-270W, and in retrospect, I could have travelled a tiny bit faster. The problem with attempting to calculate an appropriate maximum efficient speed is that we seldom know if a calculated speed/power relationship is actually achieveable due to various energy losses. Wind drag is highly variable but a major factor limiting speed on a bicycle. What to do? One can calculate a range of speed/power values and simply determine what the maximum sustainable speed/power is under existing conditions.

I wrote a simple python/Gnuplot module (maxeff.py) to plot a graph of these values. The example graph below shows the curves of max efficiency points for a range of speeds and distances for my previous trip. The goal would be to see how far up the 105 mile curve I could achieve and sustain the corresponding maximum power (Watts). If the current power I observe out on the road is below the power corresponding to my current speed, I can either increase my power until I match a speed/power point on the curve, or I can maintain that speed/power output and use less total battery capacity. The multiple distance curves help allow for changes in route, etc. and show the required fuel economy (Wh/m) to travel that distance using the specified battery capacity.

And the graph for the 36V 10Ah pack at 60% discharge covered above:

Since you can calculate efficient speed/power targets, how does that map to long-range travel capabilities?

Cycle Analyst V2.1 sneak preview describes new data logging and on-the-fly speed and current limiting features.

I recently implemented the new V2.1 code with the 10k ohm current-limiting potentiometer capability for a 260 mile trip with two 100+mile nonstop legs covering much of the same route as above. The new Crystalye 'digital' controllers are much more durable than their predecessors but suffer from a severe power surging effect at very low throttle settings, such as is needed for long-distance travelling. For a given throttle position, the new controllers often vary between about 80W and 800W, which is essentially uncontrollable at the lower power settings needed for our purposes.

This current-limiter not only made this second trip with a new-style controller possible by limiting the surging to about 60W with an average 300W power input, it removed most of the stress associated with attempting to constantly monitor and control power input. I could simply adjust the potentiometer to limit power input to the general range I needed, hold the throttle wide open, and pay more attention to the world that quickly passed by. Thanks ebikes.ca!

*May 23, 2013*