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Old 08-24-14, 10:28 AM   #1
gpo1956
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? for Mathematicians/Physicists

Which is a better more healthy workout, riding 10 miles at 5 mph or 5 miles at 10 mph?
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Old 08-24-14, 10:43 AM   #2
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The physics are that the faster ride will be more work (in the physics sense). That's because the wind resistance is proportional to the square of the speed, so the short fast ride would have you moving 1/2 the distance against, not twice but 4 times the resistance). You might not notice the difference with your 5 vs. 10mph, but try it at 10 vs. 20 and it'll be very obvious.

The health considerations are more complex. Most experts say that you need a workout that brings your heart into the so-called training range, and that it should last a half hour or more. The faster ride will bring your heart rate up higher, but may be a bit skimpy on length. OTOH the slower ride may not be strenuous enough to make much difference.

If you have a specific health related answer, the right answer depends on you rather than a formula. Discuss exercise/training goals with somebody who knows your specific capabilities and requirements.
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Old 08-24-14, 11:36 AM   #3
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An Exercise Physiology specialist or a Cycling Coach is what you need to hire .

make all those milles uphill , will be more of a workout. steeper the better ..
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Old 08-24-14, 11:47 AM   #4
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<--- Physicist grad student. FWIW, that question cannot be so simply answered, "Better" has about 10,000 different definitions and 10x as many parameters.

However, wind resistance isn't linear (link for more interest here Air Friction). So, at 2x the speed, you have 4x the drag force, all else being equal. Work is force x distance, so in the long slow case you have 5^2 * 10 = 250, whereas the short fast case you have 10^2 * 5 = 500. More work involved in the short fast.

That is the 7th grade science version, and experience agrees. Sprinting is harder than loafing .
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Old 08-24-14, 12:07 PM   #5
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5 miles @ 10 MPH = 1/2 hour workout. That's manageable.

10 miles @ 5 MPH would take 2 hours. I'd get bored and quit before I was finished.
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Old 08-24-14, 01:17 PM   #6
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Which is a better more healthy workout, riding 10 miles at 5 mph or 5 miles at 10 mph?
Walking 10 miles at 5 mph. It's really hard to ride a bicycle that slow, unless you're climbing a steep hill.
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Old 08-24-14, 02:25 PM   #7
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<--- Physicist grad student. FWIW, that question cannot be so simply answered, "Better" has about 10,000 different definitions and 10x as many parameters.

However, wind resistance isn't linear (link for more interest here Air Friction). So, at 2x the speed, you have 4x the drag force, all else being equal. Work is force x distance, so in the long slow case you have 5^2 * 10 = 250, whereas the short fast case you have 10^2 * 5 = 500. More work involved in the short fast.

That is the 7th grade science version, and experience agrees. Sprinting is harder than loafing .
Thank you. Exactly what I was looking for. The numbers were for the sake of simplicity. My area of riding is typically hilly, and I tend to try and ride 30-45 minutes at the highest pace that I can, rather than riding longer times and distances at a more leisurely pace. Not concerned about any health issues or goals, just wanting to maximize my time and efforts.
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Old 08-24-14, 04:03 PM   #8
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Walking 10 miles at 5 mph. It's really hard to ride a bicycle that slow, unless you're climbing a steep hill.
No kidding. I'd fall over...
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Old 08-24-14, 04:46 PM   #9
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Most mathematician/physicist types won't touch this because "a good workout" involves a lot of factors that aren't described by the parameters you've provided. I'm thinking primarily of bio-mechanical and physiological considerations.

Better to ask someone who is more specialized regarding fitness and exercise.
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Old 08-24-14, 05:00 PM   #10
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Which is a better more healthy workout, riding 10 miles at 5 mph or 5 miles at 10 mph?
Neither one will raise your heart rate enough to do much good. You'd be better off walking a mile or two at a brisk pace.
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Old 08-24-14, 05:28 PM   #11
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A healthy workout includes variety.

A long steady ride
An evening of intervals
A recovery ride
A hilly ride
A fast ride

Plus some cross-training.

And while I realise that the numbers used were for simplicity ...
10 miles at 5 mph on flat ground is too slow to get any sort of workout at all. You'd be better off walking/jogging 10 miles.
And 5 miles at 10 mph is really short and not very fast either. If you've only got 30 min for some exercise on certain days, intervals might be the way to go.
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Old 08-24-14, 06:02 PM   #12
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Seriously guys, let's don't over complicate this. Make the numbers whatever you want. Which will burn more calories and exert more energy? Make it 45 minutes at 18 mph or 90 minutes at 9 mph.
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Old 08-24-14, 06:08 PM   #13
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Seriously guys, let's don't over complicate this. Make the numbers whatever you want. Which will burn more calories and exert more energy? Make it 45 minutes at 18 mph or 90 minutes at 9 mph.
You got the answer a while back, from myself and others. Twice the speed for half the time ends up doing twice the work. Then as long as the workout is long enough for residual effects you'll reap greater benefits, though not necessarily twice as much.

East way you can confirm this for yourself. Do both rides and see which leaves you more tired. Low level exercise can be sustained almost indefinitely and doesn't product an exercise benefit. High level exercise that stresses your system and cannot be sustained for long periods does.
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Old 08-24-14, 06:45 PM   #14
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I ride/train the way Machka does, variety.
There is no simple "physics" answer to this, perhaps you are asking the wrong question.
I only go for a long low mph ride as a recovery ride, this takes several hrs and several miles.
The next day I ride for only an hour, but it is an hour riding the same hill which has a 13% grade and has a cobble stone road and is about 1/2 mile long.
That is a great workout.
The recovery ride is 50++ miles, while the hill ride may only be about 5 miles.
Your question really don't make any sense.
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Old 08-24-14, 08:14 PM   #15
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You got the answer a while back, from myself and others. Twice the speed for half the time ends up doing twice the work. Then as long as the workout is long enough for residual effects you'll reap greater benefits, though not necessarily twice as much.
Depending on different variables, it takes about 5 times as much power to do 18 mph compared to 9 mph. So, it might be closer to 2.5 times as much. If anybody really wants to answer the question from a physics point of view, I'd recommend a bike power calculator (my favorite is this one:An interactive, model-based calculator of cycling power vs. speed).
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Old 08-25-14, 08:21 AM   #16
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Which is a better more healthy workout, riding 10 miles at 5 mph or 5 miles at 10 mph?
OP; [ Recommended alternative would be a healthy young GF ... great workout at any speed and any distance... just sayin' as you can ride the bike later in life
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