POWER CALCULATION

POWER CALCULATIONS:

POWER CALCULATIONS
A how:
to find the energy needs of your function or device.

To calculate the energy needs for you application you need to figure out the ENERGY used over TIME (as WORK) which is the POWER.

E/T = Power

ENERGY-> is a potential to do work but is static because:
While one form of energy may be transformed to another, the total energy remains the same.

POWER-> is the rate at which work is performed or energy is transmitted.

a good tutorial on the difference is here:
http://www.glenbrook.k12.il.us/gbssci/phys/Class/energy/u5l1a.html

A common method for understanding and converting the total energy use of a system is by transferring the original work or power rating into joules and then comparing.

-WORK(or POWER)is usually described in WATTS: (1 watt) * 1 sec = 1 joule.

-ENERGY is described in JOULES: (1 joule) / (1 sec) = 1 watt.

A WATT (http://en.wikipedia.org/wiki/Watt) is a measurement of Work: it is the (Amperage * Voltage) used in one second and is equal to the use of 1 joule of energy per 1 second.

The JOULE (http://en.wikipedia.org/wiki/Joule) is the base standard of energy and can be converted to just about any energy/force related issue.

You can do this conversion with kinetic work
kinetic examples of finding power used
http://id.mind.net/~zona/mstm/physics/mechanics/energy/energy.html

or electromagnetic work

http://www.swansontec.com/set.htm

http://www.glenbrook.k12.il.us/gbssci/Phys/Class/circuits/u9l2d.html

or thermal
http://hyperphysics.phy-astr.gsu.edu/Hbase/thermo/heatra.html

CONVERSION EXAMPLE:

For instance:
lets say you wanted to design a system that lifted a 4Kg bowling ball a height of 5 meters using a solar panel motor and a micro controller. you would calculate

FIRST
CALCULATE POWER NEEDS

First: power needed to raise the bowling ball:

First we calculate the difference in energy potential of the bowling ball when moved a height of five meters.This will show us the energy we have to put into the bowling ball to raise it to the new potential ( it is gauged by the New stored energy - the Old stored energy).

Ug (gravitational potential energy) = mass*gravity*height

196 joules = (4 kg)(9.8 m/s/s)(5 m);

SECOND
CALCULATE TIME PERIOD

Second: Since WATTS or Power is the transfer of Energy over Time we then have to add in a time scale that the process is going to take, to find the power use.

So lets say you wanted to do it in one second,

you take the energy potential in joules (196) and spread it out over one second(196/1) which is the definition of 1 Watt(1 watt = 1 joule /1sec) so:
(196/1sec) = 196 Watts

So your motor will chew up *196 Watts of power lifting the weight.
*plus the internal friction loss of the motor.

THIRD
CALCULATE MISC. POWER LOSS

THIRD: you would have to calculate what the power needs of your micro controller are (See here for more on figuring out energy needs of electronic components) and this is done in electrical work (power) terms;
Lets say your using a atmel atmega 168 to do the logic, you would have to look at the data sheet to see what the operating power costs were for that chip (this all depends on the clock speed and running voltage) but lets say your running it at
3.3 Volts and it is drawing 20ma of continuous power.

We can take those numbers and turn them into the power use in watts.

*for a complete overview of electricity use this link it is an AMAZING web site:* http://williamson-labs.com/

and here (http://www.onlineconversion.com/) for the conversions of amps to milliamp. OR just type "1 amp in milliamps" into a google search box it also does almost any conversion you want (tip from Jeff Federson).

VOLTAGE * AMPERAGE = WATTS

1V * 1AMP= 1 WATT

This gives:

3.3V * .020A (20ma) = .066 watts

So, to run it for one second it would take:

.066 Watts * 1 sec = .066 joules

You can now add up the watts or the joules to find the total power or energy needed:
196 Watts motor + .066 watts micro controller = 196.066 watts of constant power.
or
196 joules + .066 micro controller = 196.066 joules of potential energy needed for X amount of time.

In designing the system you would then need to get a solar panel SOLAR PANEL power calculation LINK or other device that can give you a continuous 196.066 watts per second or design a system that can store up (in a battery or capacitor) POWER STORAGE LINK 196.066 joules of potential energy.

As an example the
Will O' the Wisps power
needs were calculated as follows:

For the Will o the wisp moduals I broke the system up into three parts;
the first part was the power system for the logic and function controls (microcontroller frequency generation and turning moduals on and off), the second was for the amplification of the sound and driving the speaker, third was the power needed for the charging of the batteries.

I split these into separate systems because each had a different power need and use.
The charging circuit needs a small current only when there is power to put into the battery.
The speaker/amplifier will take in a unregulated source with and has much higher current draw but only needs it for intermittent short bursts.
The logic control system needs a regulated constant small current.

The first is the battery charging system which takes the variable solar energy

and regulates it in order to cause the appropriate chemical reactions in the batteries.This process allows the battery to developer a voltage which that can then be used as a constant source of power later.
The charging system requires 5-36volts to operate and will draw 6ma of current for the circuitry to operate so the available power will always be:
INPUT-6mA

for charging circuit
3 mAfor 555 chip
1 mA for comparator
2 mA for transistors + voltage divider
6 mA total

The second system is used for the logic and RF communication. This system needs to be tightly regulated in order to keep the RF and logic functioning properly. The system runs off the battery bank which is then regulated by a LM low dropout 3.3 voltage regulator. The battery bank is charged to 4.8Volts and the regulator can give 3.3V @100ma with a drop out voltage of 130mV (which means it will provide a 3.3 voltage using the battery as long as the battery is in the range of 4.8v-3.43v), this gives a powerful second layer to keeping the power supply constant.

Power usage overview of components
Digital pot 500 uA
TIP 120 *whatever you put in base
TC1262-3.3vab 80 uA
TS 555 100uA
LM386 4 mA
LM339 800 uA
Atmega168 8mA
xbee 40mA

total:

53.48mA

battery size considerations

The battery bank is comprised of 4 AA batteries which are rated at 2100mAh, this was chosen to balance the solar panel which supplies a 300ma maxium output . so:
300 mA (solar supply)*8 hours = 2400 mA - (50mA*8 usage)
gives a possible 2000mA of storage for a day of super equatorial sunlight.
and a full battery could run the logic
total storage /8 hours of use a day gives:

2100mA/ (50mA*8hours)= 5.25 days of operation off a full charge.

The third system runs off a bank of 2.7 3F ultra capacitors which feeds into the lm386 amp driving the speaker. This system is directly charged from a separate solar panel, i kept this separate for two reasons first to cut down on the noise of pulling 200mA off the same circuit as the logic source. Second is conceptual, it is interesting to see the current changes in the available solar energy by not averaging it out as much over time. This allows the system to show threw the ability and volume of the speakers playing which module is doing well in terms of power.

200 ma for amp+speaker (intermittent on a separate system)