I feel sure I have miscalculated here. Can anyone shed any light on it?

[Tringa]

Last Tuesday here in NW Scotland was superb, so good that if it had been in June people would have commented about how warm it was, so I decided to go for a walk.

One of the things I wondered about on the walk was much energy I had used. I realised I would have to make a few approximations and ingore a number of things so I decided to concentrate only on the energy needed to move me vertically.


The energy (in Joules) needed to lift a mass =


Mass x acceleration due to gravity x the height


I weigh around 83kg, acceleration due to gravity is about 9.8m/s/s and the height was about 867m.

This means to get raise me by 867m took about 705,218J.


What is that in Calories? These are nutritional calories, ie the ones used on foods. A Web based conversion -

http://www.convertunits.com/from/joules/to/calorie+[nutritional]

says 705,218J is about 168 Calories, which is about the same energy you'd get from two chocolate digestive biscuits.

This seems very small especially as other calculators on the Web suggest walking a mile (I assume they mean on the flat) at about 2mph uses about 103 Calories.

Have I made a mistake in my calculation?

Dave

 

[PaulF]

Not sure, but I bet you can get an app for that

 

[B1ts]

Yes, you didn't just move vertically
Hth.

 

[Deleted member 49549]

EDIT

You are assuming a 100% mechanical efficiency. The reality I would guess to be a lot less than that, being one of the larger missing elements in your calculation.

 

[BRASH]

Both my treadmill and running app on my iPhone tell me I'm doing between 150-170 cals per mile both walking and running. The treadmill is the slightly higher because I have it at a constant incline so I reckon your calculations ain't far off the mark.

 

[StewartR]

Your calculations, including the conversion from Joules to Calories, are technically accurate. But fairly meaningless, as others have said, because you're expending energy to do a lot more things than just elevate your body vertically.

 

[omens]

Not quite accurate because of the way you calculated it because you're talking about the human body. In physics, you need energy to move something against gravity. When you're moving down, it's gravity doing the work. In either case, it's better to think of it as "potential energy". PE=mgh

When you walk up a slope, you'll expend biological energy but you'll gain potential energy. When you then jump off the cliff, gravity does the work and the potential energy gets converted into kinetic energy.

 

[JonathanRyan]

I realised I would have to make a few approximations and ingore a number of things so I decided to concentrate only on the energy needed to move me vertically.

That right there is your problem

It's very very difficult to work out how many calories any exercise takes - especially one with as many variables as walking.

For example, I did a 10 mile race last week. I wore a heart rate monitor and GPS watch. My watch knows various extra factors like my weight and cadence and also has a barometric gizmo to work out when I'm going uphill so it knows how much weight I'm lifting and how high. I.e. it knows a lot more than the numbers you put in. One app (Suunto Movescount) says that I used 1,200 calories. Another (Strava) using exactly the same data calculated it as 1,300. I had a sugary shake and a bag of chips at the end and honestly probably ate more calories than I had burned.

Oh and don't forget your basal metabolic rate - at a rough guess if your walk took an hour you also burnt 70 calories just by breathing etc.

 

[Tringa]

Thanks all.

My thinking was

(a) how can walking a mile fairly slowly use about 2/3rd of the Calories I used to get up the hill(as some of it, especially the last 400m was hard work), and
(b) if going up 867m uses only 168 Calories, why do I need over 1,000 Calories a day.

However, as you folks have pointed out, there is a lot more involved and I'm, incorrectly, comparing the simple physics calculation (energy to raise a mass by x metres) with the more complex calculation of Calories used by the human body.

Cheers

Dave