Pace Factor: Calculating The Approximate Distance You’ve Walked (Complete Tutorial And Calculations)
Time is important, in fact, the classic proverb is still echoing “time is gold.” We are too much liable on how we spend our time. To some, when they walk, they are texting. Others, are just letting their minds go wander around things. But why not consider walking as a fun and exciting game. Try calculating the approximate distance you have traveled on foot, no not using a meter stick or a measuring tape, but simply using your pace factors.
Let’s have a game
Consider it as just a game. You move from one place to another, and in some other time, circumstances might require you to determine the approximate distance you have covered. And to think of it as a game, you'll end up in gladness that you did not just arrive, but estimated how far you have walked. No time wasted!
Forget about being so techie this time, letting our brains do the hard work and not our phones. Forget about GPS and other apps, because we are going to use the pace factor.
What is pace factor?
Pace factor is normally discussed in surveying classes, but its application is not just for engineering students. Anyone who is willing to be quantitative and loves knowledge will consider it to be a plus factor in life. And hey, you don’t have to bother since you don’t need to be a math genius first before you can do this.
Pace is defined as a single step taken when walking or running. And pace factor is simply the ratio of your paces over time. Let me show you by definition what pace factor is by this 3 methods: (1) pace per meter, (2) meter per second, (3) pace per second.
1. Pace per meter factor (PpM)
Paces per meter (PpM) is the factor derived from dividing the total number of paces to the total number of distance covered. In simple words, it is the number of paces every 1-meter distance.
PpM requires a lot of concentration since you have to count every step you’ve made throughout the distance. And what if someone calls or distracts you along the way? I tried it, and it’s frustrating. I can say that PpM is best for short distances.
In surveying, PpM is often introduced. Like I said, such method requires a lot of concentration, especially when you’re into a long walk. That’s why I added 2 more factors for convenience. You can actually choose your own preference.
2. Meter per second factor (MpS)
The meter per second (MpS) is the factor derived from dividing the total distance walked to the total time covered. It is the number of ‘meters’ in every 1-second time. This factor is simply your speed.
It’s better than PpM since you don’t have to count your steps. And what if someone calls you along the way? I tried it, and what I did was paused my stopwatch, run it again after I’m done talking, and I continued walking.
I can say that MpS is best for long-distance walks.
3. Pace per second factor (PpS)
The pace per second (PpS) is the factor derived from the two previously known factors. But it could also be derived separately from dividing the total paces to the total time covered.
PpS cannot solve the distance traveled alone. It must use one of the two factors to get it. For me, this factor is best when determining the approximate time you have walked even without knowing the distance.
The procedure is simple. Let’s get that step by step.
Step 1: Get the distance between two points
Step 2: Make 3 trials to get pace and time
Step 3. Average the results
Let’s have a game
Consider it as just a game. You move from one place to another, and in some other time, circumstances might require you to determine the approximate distance you have covered. And to think of it as a game, you'll end up in gladness that you did not just arrive, but estimated how far you have walked. No time wasted!
Forget about being so techie this time, letting our brains do the hard work and not our phones. Forget about GPS and other apps, because we are going to use the pace factor.
What is pace factor?
Pace factor is normally discussed in surveying classes, but its application is not just for engineering students. Anyone who is willing to be quantitative and loves knowledge will consider it to be a plus factor in life. And hey, you don’t have to bother since you don’t need to be a math genius first before you can do this.
Pace is defined as a single step taken when walking or running. And pace factor is simply the ratio of your paces over time. Let me show you by definition what pace factor is by this 3 methods: (1) pace per meter, (2) meter per second, (3) pace per second.
Paces per meter (PpM) is the factor derived from dividing the total number of paces to the total number of distance covered. In simple words, it is the number of paces every 1-meter distance.
PpM requires a lot of concentration since you have to count every step you’ve made throughout the distance. And what if someone calls or distracts you along the way? I tried it, and it’s frustrating. I can say that PpM is best for short distances.
In surveying, PpM is often introduced. Like I said, such method requires a lot of concentration, especially when you’re into a long walk. That’s why I added 2 more factors for convenience. You can actually choose your own preference.
2. Meter per second factor (MpS)
The meter per second (MpS) is the factor derived from dividing the total distance walked to the total time covered. It is the number of ‘meters’ in every 1-second time. This factor is simply your speed.
It’s better than PpM since you don’t have to count your steps. And what if someone calls you along the way? I tried it, and what I did was paused my stopwatch, run it again after I’m done talking, and I continued walking.
I can say that MpS is best for long-distance walks.
3. Pace per second factor (PpS)
The pace per second (PpS) is the factor derived from the two previously known factors. But it could also be derived separately from dividing the total paces to the total time covered.
PpS cannot solve the distance traveled alone. It must use one of the two factors to get it. For me, this factor is best when determining the approximate time you have walked even without knowing the distance.
How
to get your pace factor
The procedure is simple. Let’s get that step by step.
Step 1: Get the distance between two points
- Get a tape measure (or any equivalent) and choose a good location with a flat terrain.
- Measure and mark two (2) points in a straight line (in meters) using the measuring tape. Remember that the longer the distance between the two points, the better the results.
Step 2: Make 3 trials to get pace and time
- From the first point in the line, simultaneously count and time (in seconds) your pace using a stopwatch. Just walk the normal way you walk. Don't be bothered by counting. If it helps better to have someone to assist you, then do it.
- Record the total number of paces and time duration.
- Make at least two or more trials.
Step 3. Average the results
- Average the results for paces and time separately.
- Consider my example below to calculate the pace factor.
Pro tip:
To make your measurement simpler, choose a less traffic segmented concrete road in your area. Just measure one road segment and multiply it to the number of road segments you like. Normally, each road segment has the same length. The resulting product is your total distance for the experiment.
One thing though, when it comes to pace factor, you need to remember that, the terrain (uphill, downhill, etc.), its surface (concrete, slippery, etc.), your footwear, your load carried, the weather, your companion, your emotion, the road obstructions and distractions, are likely to affect your normal walk which in return can affect the results.
It may be necessary to have as many pace factors per condition. But you don't have to bother. What is important is to have your normal pace factor for your day-to-day normal walk.
Consider my experiment
I tried mine with 24.8-m distance between marked two points (measured from a 3.1-m concrete road segment). From that distance I had 3 trials: 55 paces in 32 sec.; 56 paces in 34 sec.; and 56 paces in 32 sec. By averaging the results of the 3 trials, I got 55.67 paces in 32.67 sec.
The table below shows how it was done.
To make your measurement simpler, choose a less traffic segmented concrete road in your area. Just measure one road segment and multiply it to the number of road segments you like. Normally, each road segment has the same length. The resulting product is your total distance for the experiment.
One thing though, when it comes to pace factor, you need to remember that, the terrain (uphill, downhill, etc.), its surface (concrete, slippery, etc.), your footwear, your load carried, the weather, your companion, your emotion, the road obstructions and distractions, are likely to affect your normal walk which in return can affect the results.
It may be necessary to have as many pace factors per condition. But you don't have to bother. What is important is to have your normal pace factor for your day-to-day normal walk.
I tried mine with 24.8-m distance between marked two points (measured from a 3.1-m concrete road segment). From that distance I had 3 trials: 55 paces in 32 sec.; 56 paces in 34 sec.; and 56 paces in 32 sec. By averaging the results of the 3 trials, I got 55.67 paces in 32.67 sec.
The table below shows how it was done.
Step 1. Get the distance between two points
|
Distance = 24.8
meters
|
||
Step 2. Make 3 trials to get pace and time
|
Trial
|
Pace
|
Time
|
Trial 1
|
55.00
|
32.00
|
|
Trial 2
|
56.00
|
34.00
|
|
Trial 3
|
56.00
|
32.00
|
|
Step 3. Average the results
|
Average
|
55.67
|
32.67
|
The table below shows the data I acquired.
Data acquired
|
|
Distance (meters)
|
24.80
|
Average pace
|
55.67
|
Average time (seconds)
|
32.67
|
Now to get my PpM, I divided the average paces to the total distance (i.e. 55.67 paces / 24.8 m). My resulting PpM was 2.24.
For MpS, I divided the total distance to the average time (i.e. 24.8 m / 32.67 sec.). My resulting MpS was 0.76.
For PpS, I just multiplied my MpS and PpM and I got 1.7 PpS.
The table below shows how it was done.
For MpS, I divided the total distance to the average time (i.e. 24.8 m / 32.67 sec.). My resulting MpS was 0.76.
For PpS, I just multiplied my MpS and PpM and I got 1.7 PpS.
The table below shows how it was done.
Pace Factor
|
|
Pace/meter (PpM)
|
55.67 / 24.8 =
2.24
|
Meter/second (MpS)
|
24.8 / 32.67 =
0.76
|
Pace/second (PpS)
|
2.24 x 0.76 =
1.70
|
Useful formulas
Based on your pace factors, we can now derive the following formulas:
To compute the distance walked:
Where,
P = number of paces covered
T = total time of travel
D = distance traveled
PpM = pace per meter factor
MpS = Meter per second factor
PpS = pace per second factor
Consider this example calculation
Problem: A clever native boy goes to school everyday in a remote plains in the Philippines. He walks 2 hours everyday just to go to school. The boy has a pace factor of 0.76 MpS. How far is his school from his home?
Solution:
Based on your pace factors, we can now derive the following formulas:
To compute the distance walked:
(Eq. 1)
|
D = P / PpM
|
or
(Eq. 2)
|
D = T x MpS
|
To determine the time travelled:
(Eq. 3)
|
T = P / PpS
|
P = number of paces covered
T = total time of travel
D = distance traveled
PpM = pace per meter factor
MpS = Meter per second factor
PpS = pace per second factor
Consider this example calculation
Problem: A clever native boy goes to school everyday in a remote plains in the Philippines. He walks 2 hours everyday just to go to school. The boy has a pace factor of 0.76 MpS. How far is his school from his home?
Solution:
Data acquired
|
|
Distance
|
Unknown
|
Pace factor
|
0.76 MpS
|
Time traveled
|
2 hours
|
Using the formula in Eq. 2,
D =
|
T x MpS
|
=
|
(7,200 sec.) x (0.76 MpS)
|
=
|
5,472 m
|
D =
|
5.5 km
(Approx.)
|
Suggested application
We can have a variety of applications for this. The best application is for education especially if you're teaching STEM subjects. This is also a great way to introduce engineering principles to aspiring young builders. Also, you might want to use this as your Math project for competition and display.
Doth not he see my ways, and count all my steps? John 31:4
We can have a variety of applications for this. The best application is for education especially if you're teaching STEM subjects. This is also a great way to introduce engineering principles to aspiring young builders. Also, you might want to use this as your Math project for competition and display.
You might want to use it as a pastime with friends. You can introduce it as part of a treasure hunting activity. You can even do team building activity for this. Hiking, trekking, try it now, and enjoy the game.
