Bicycle power

A few months back, Deepak Malani asked me about the torque and power requirements of a bicycle so as to get an idea of the required ratings of an electric motor that can be retrofitted in the bicycle. So I went about doing some back of the envelope calculations taking into account rolling friction, aerodynamic drag and inclines. Here's a simple MATLAB/octave script I wrote to carry out the calculations.

The following assumptions were made:

• The transmission (pedal-sprocket-chain assembly) is 100% efficient. Note that practical efficiencies are in the range of 96-98%
• The rider plus bike system is moving at a constant velocity
• There is no headwind, tailwind or crosswind

Plugging in some typical values for the parameters, a 65 kg rider on a 15 kg bike moving at 15 kmph on a level road (no incline), does mechanical work at a rate of 60 Watts. He/she would need to put in a torque of about 10 Nm into the pedals (assuming a gear ratio of 2).

You can use the script for plugging in various values of the parameters and compute the torque and power requirements under those conditions. Note that at even a couple of degrees of upward incline, the torque required to overcome gravity dominates over that required to overcome rolling friction and aerodynamic drag.

The computations in the script are for a constant speed. However, the rating of the motor needs to take into account the worst case scenario which would typically be an acceleration or even a constant speed climb up a specified incline.

A few points to note:

• Coefficient of rolling friction (Crr) could vary between 0.0021 to 0.017 [1]
• Aerodynamic drag coefficient (Cdr) could vary between 0.65 to 1.1 [1]
• Gear ratio (GR) could be anywhere between 1.75 to 4 [2]
• The gear ratio (GR) and wheel radius (Rw) effect only the torque requirement but not the power requirement
• For electric bikes with hub motors, GR=1

References:
[1] Stetler, Energy Efficiency of Bicycle Transportation
[2] V. Ryan, The Basics - Gear Ratio
[3] Ashburn, The Physics of Moving a Bike
[4] Cycling Aerodynamics & CdA - A Primer

Energetic consequences of doing things slowly

From charging capacitors to filling up water tanks.

Electrical engineers are familiar with the idea that when you try to charge a capacitor from a step voltage source, only half of the energy coming from the source gets into the capacitor while the other half is dissipated in the circuit resistances and/or lost as radiated electromagnetic energy. In other words, the efficiency is only 50%. Does it always have to happen that way? How can we do better?

The answer lies in shaping the applied voltage. If the rate of rise of the applied voltage is of the order of the time-constant of the circuit, the efficiency is much better than 50%. If it is very slow compared to the time-constant of the circuit, the efficiency approaches 100%. This is proved analytically as well as validated by circuit simulation in this article.

Even if we did not shape the voltage, if the capacitor doesn't have a linear relation between charge and voltage (in other words, it is a non-linear capacitor), the efficiency can still be very different from 50%.

The case of a step current source feeding an inductor is also analogous to the above scenario and gives similar results.

Taking a step back and applying this concept to any other domain (other than electrical engineering) can give some interesting insights. Pumping water into an overhead tank through a pipe having finite resistance (due to friction) is an example of an effort source feeding a potential energy storage element much like a voltage source charging a capacitor. Hence, it will take lesser energy if we were to pump the water slowly (trickle pumping) over several hours rather than doing it fast (gushing water) in fifteen minutes flat!

On a philosophical note, a very nice example is that of a teacher teaching a student. If the teacher goes far too fast beyond the grasping speed of the student, much of the knowledge doesn’t get transferred to the student’s brain.

Sleep Detector Power Saver

I remember umpteen instances when I've seen people leave their lights and/or televisions turned on and fall asleep. While the person is recharging himself his appliances are continuously hogging power all night for no useful purpose at all. Of course the easiest solution to the problem is for people to realize the mistake and be responsible enough to turn off all unwanted utilities when they go to sleep.

But since we still have so many careless people around, there is a potentially huge market for a product that could detect sleep in a person and take action accordingly - switch off lights, TV etc. Sleep detection could be done based on monitoring of one or more of various parameters - heart rate or pulse rate, body movement, body temperature, respiration rate etc. The major challenge in such a product would probably be to identify which among these myriad options would provide the cheapest and the most reliable way to detect sleep. Any answers?

[This post is an elaboration of Problem-3 on the post "Nine Problems Worth Solving"]

Ceiling fans can do better

A typical 75 W-input ceiling fan only generates about 15 W of mechanical power, making it only 20% efficient. The balance of 60 W is dissipated as heat.  Winner of Farnell’s Live EDGE design contest, John Nobel identified this problem and tried to solve it. He designed a product called MyFan, a ceiling fan that combines an electronically commutated motor and controller, and aerodynamically efficient blade design that reduces fan input power by up to 66 percent of that of a traditional ceiling fan. In other words, the new design is three times as efficient as the conventional design. It boasts auxiliary output channels that drive up to 20 watts of integrated LED lighting with up/down lighting modules. The motor construction is totally enclosed and is available with an IP5x environmental rating. Here's an article that highlights the achievement. 

Ceiling fan design promises reduced power consumption

Recently chosen as the grand prize winner of distributor Premier Farnell’s Live EDGE design contest, a ceiling fan dubbed MyFan by designer John Noble combines an electronically commutated motor and controller with an aerodynamically efficient blade design to promise input-power reductions of up to 66% over traditional ceiling fans. Noble, a Malaysia-based design engineer, came up with the idea in early 2007, before he even heard about the contest, which he ultimately found out about the through Farnell’s Web site while placing an order in May 2007.

Premier Farnell CEO Harriet Green presents a $50,000 check to John Noble, winner of Farnell’s Live EDGE design contest.

On hiatus from his job, Noble had been pondering how to move his career toward efforts that were more socially or environmentally focused. The answer, as it turned out, was closer than he knew.

“In our house we have nine ceiling fans, and at any time of the day or night there are at least three of those running,” he said. “Quite literally the first thing see every morning when I wake up is a ceiling fan. One morning I woke up and decided I should have a closer look.”

While ceiling fans have been on the market for over 100 years, their motor design has really changed very little. And current fans are terribly inefficient. According to the award-winning designer, a typical 75-W-input ceiling fan only generates about 15 W of mechanical power, making it only 20% efficient. The balance of 60 W is dissipated as heat.

A fan constructed with modern components—specifically electronically commutated motors—has an efficiency of about 60% reducing input power to about 25 W to offer drastic power-consumption reduction.

Noble’s research shows that in the United States alone, there are about 158 million ceiling fans installed consuming 150 petajoules (PJ) annually. Fans designed with the high-efficiency ac motors can reduce that by about 100 PJ and eliminate 14 million metric tons of CO2 emissions.

While the technology could be applicable for other types of fans, this particular design is focused on the specific characteristics of ceiling fans. “It is a relatively low-absolute-power module that generates quite high torque at low speeds,” Noble said. “Generally, industrial fans tend to operate at higher speeds and draw more power.”

Suprisingly, Noble used Microsoft Excel for the bulk of the design effort. “I do most of my electronic circuit analysis actually using Excel, which now has a wide range of features that allow very good simple numerical analyses to be done,” he said. “I did 3-D and mechanical design using Alibre Design Software, I used a company called Field P for doing magnetic field simulation, and circuit-schematic capture and PCB layouts are done on [Altium’s] Protel.”

Premier Farnell plans to present another design contest for 2008. For more information about the contest, visit http://www.premierfarnell.com.

Ralph Raiola

(source: http://www2.electronicproducts.com/Ceiling_fan_design_promises_reduced_power_consumption-article-olrr01_mar2008-html.aspx)

Using advanced motor control algorithms such as field-oriented control or vector control could further improve the efficiency, though I'm not sure whether Nobel's design already incorporates such an algorithm. The Indian fan market is estimated at 2.5 million fans per month and it is growing at about 10% per annum [1]. Also, there are currently several millions of fans that have percolated down to the millions of households in India. Incorporating energy efficiency into them could lead to huge savings in power. The Bureau of Energy Efficiency (BEE) in India is to shortly issue a notification suggesting raising of energy efficiency parameters for fans manufactured in the country. The implementation of the new standards would help save between 15 and 20 per cent electricity in new fans while conserving over 30,000 MW of electricity over the next five years in the country[2]. We can do even better if we were to take a cue from Noble's work. Is there an enterprising entrepreneur somewhere who's listening?