Welcome to The STEM Sessions Podcast. I am your host, Jarl Cody.

I’ve spent my share of time hiking and backpacking on local trails and in the backcountry

Over the years, I’ve pick up rules of thumb that help you estimate how much daylight you have left and how the temperature will change as you climb or descend elevation, just to name a few

But recently I was introduced to a new one, or at least new to me

In Dave Canterbury’s YouTube video published May 17, 2023 (link in the shownotes), he shares a rule of thumb for estimating distances between you and a target

While Dave offers a great how-to explanation for this rule of thumb, his video doesn’t explain why it works in the first place

This caused me to raise a People’s eyebrow of uncertainty

It just seemed too easy to be true, and while that is a confirmation bias unto itself, anytime something is presented in a “just trust me” fashion makes me want to prove it to myself even more

So that’s what I’m doing here.

I’m doing the work to prove or disprove this rule of thumb, so I know if it can be relied upon the next time I’m off trail in the backcountry

This is The STEM Sessions Podcast Episode 23 – Thumbing For Distance

Despite not having a definitive origin, phrase “rule of thumb” dates back to the 1600s

- Most likely referred to using one’s thumb to represent an inch in measurements
- Today, it can be used for any method of approximation
- Typically a method that is easy to remember
- Short cut to results, based on repeated practical experiences rather than application of theory or calculations

We use many rules of thumb in STEM and in day to day life, but we rarely ask why the rule of thumb works

- Just assume it’s good enough
- Why would it be a rule of thumb if it wasn’t correct?

Learned a new rule of thumb, one for estimating the distance to an object

- Involves extending your arm in front of you with your thumb pointing up
- With one eye closed, sighting down your arm, and move your arm such that your thumb is just to the side of the target or on the middle of the target
- Then close that eye and open the other
- As you do this, your thumb changes position relative to the target
- You estimate the number of target widths your thumb travels
- Multiple that by your best guess as to the objects true width
- Then multiple by 10
- Result is the distance to target

I’ll leave it to you to watch the original youtube video for a clearer explanation

Multiply by ten immediately struck me as too easy to be accurate

- Accuracy is important even in rules of thumb, especially one involving distance to target
- Decided to determine how close 10x really is

Familiar with navigating trails with map and compass

- Plotting a course using triangulation between points is a common tool
- While that’s not exactly what we’re doing here, I had a feeling triangles and plotting would be a good place to start

Pictured a piece of graph paper with me standing on point (0,0)

- Target would be at point (0,D) where D is distance to target
- When i outstretch my arm, my thumb is at point (0,A) where A is my arm length
- When i switch eyes, my thumb moves a multiple N of the target width W
- This point is (NW,D)
- When you close one eye and open the other, you’re shifting the origin point the distance between your eyes to point (-E,0)

Your sketch now has two triangles

- One is from your thumb ((0,A) to to target (0,D) to your projected thumb (NW,D)
- Other is from your thumb (0,A) to your first eye (0,0) to your second eye (-E,0)

To relate these triangles, the rule of alternate angles tells us the angles converging at point (0,A) are equal

- Tangent of angle is length of opposite side divided by the length of the adjacent side
- first triangle, tangent of the angle is NW divided by quantity D-A
- Second triangle, tangent is E divided by A

Set these two quantities equal to reach other and solve for D

- Result is A plus A divided by E times NW

two conclusions from this equation

- Results will technically vary from person to person because arm lengths and eye separation varies
- As distance to target increases, the term with only arm length becomes less important

Now, let’s focus on the validity of the 10X multiplier

- this is corresponds to A divided by E
- So is the length of ones outstretched arm 10 times longer than the distance between their eyes

Distance between your eyes is called pupillary distance

- You’ll find it on your glasses prescription if you have one – though it wasn’t on mine
- Technically there are two pupillary distances; near and far pupillary distance
- When looking at something up close, eyes point inward and near pupillary distance can be 3 to 4 millimeters shorter than far pupillary statue l distance
- Far pupillary distance is applicable to this discussion

average adult pupillary distance is 62 mm, with a normal range roughly 10 mm to either side

- Can vary along Gender, ethnicity

Average adult arm length, or more accurate the distance from eye to thumb, is difficult to find

- To achieve the 10x multiplier, distance between thumb and eye would need to be 62 cm or 24 inches.
- For reference, i measured my eye to thumb distance to be a bit over 23 inches or 59 cm
- I’m right at six feet tall, which is a bit above average so i would expect my arms to be a bit above average length

This tells me 10x is an over estimate

- Account for variation in anatomy
- when judging distance, probably better to overestimate; fewer negative repercussion
- Plus, uncertainty in estimating target width and thumb displacement
- I suspect people would underestimate these variables more than overestimate so using a larger multiplier likely compensates
- Plus, 10X is easy to do in your head so its intended to make the math easier

For completeness, my pupillary distance is 64 mm and my eye to thumb distance is around 590 mm

- So my personal multiplier is closer to 9, about 9.2
- I plan to run controlled experiments in the field to see how close this prediction might be
- Results will be featured on another episode
- For now this exercise has given me confidence this rule of thumb for estimating distance has some mathematical basis and isn’t grossly wrong
- Have no problem using it the next time I’m on a trail, and no problem recommending other people use i

Using a rule of thumb blindly is ok most of the time, but there are always exceptions to the rule

- Understanding the background and basis of the rule of thumb is critical to understanding when you can count on the rule and when it shouldn’t be used
- Plus, it’s just satisfying to know why it works in the first place

Thank you for listening to The STEM Sessions Podcast.

This episode was researched, written, and produced by Jarl Cody.

Here at The STEM Sessions, we strive to share accurate and complete information, but we also encourage you to do your own research on the topic we discussed to confirm the accuracy of what we’ve presented. Corrections are always welcome.

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Finally, please remember STEM is not a tool exclusive to experts, policy makers, and talking heads. Every presenter is susceptible to unconscious and, sometimes, deliberate bias, so always verify what you read and what you’re told.

Until the next one, stay curious.

REFERENCES

Rule of Thumb ESTIMATE DISTANCE