Bicycling

I am confused for the difference may be the difference on what the two devices are measuring:

Reason for the difference: Situation one - the two tools you are using are measuring two different things:

I use an old fashion electronic "Computer" that uses a magnet on the wheel and counts the turns of the wheel to produce an accurate measurement of miles. I have an app on my phone that uses GPS to measure mileage. Given that the measurement may be off up to 100 feet I fully expect the two NOT to read the same.

The Wheel based system is measuring actual movement, the APP is measuring movement in relations to up to 23 satellites.

This is related to the difference between Acceleration and Instantaneous Acceleration. People tend to view them as the same thing, but they are different AND the measurements from both system tend to be close, but different.

A wheel base computer is using normal Acceleration, that is the increase in Velocity over a time period. Instantaneous Acceleration is what a Radar gun measures, how fast you are going that very instant. I suspect any GPS based mph system is measuring Instantaneous Acceleration over and over again. Thus it is constantly changing. The same with normal acceleration, as you speed up and slow down the "speed" being measured changes. You do not see it but each time the reader goes by the magnet you have a new normal acceleration, thus normal acceleration is also constantly changing.

http://physics.info/acceleration/

Thus the difference may be do to the simple fact you are using two different method of measuring your speed. These two systems are NOT the same nor are their measuring the same thing. Both uses mph (or Kph) but that is all they have in common. The numbers from both systems tend to be close, but rarely the same for their are measuring two different things.

Reason for the difference - Situation Two 0 - Errors in measurement

While a wheel based measurement system tends to be very accurate (in the sense it is constantly measuring the same thing, but at different speeds), GPS system have error rates based on the fact that it is receiving signals from Satellites, and the system was designed with an inherent error rate. Most GPS system can deal with this error rate, but it takes additional electronics that most people do not need. For example the Military has each Satellite use two different frequency, while the Civilian GPS only reads one of those frequency.

http://www.gps.gov/systems/gps/performance/accuracy/

As to most users of GPS, does it really matter if you are 10, 20 or 30 feet from where you want to be? As a biker you can quickly make up that difference.

We do not need that type of accuracy, most GPS system will determine if you off your route by the time you had driven 50 feet and make corrections. Many will correct to even closer tolerances if your GPS device has signals from all of the Satellites.