Is there an equivalence in running?

So this is a bit of an odd question but at what point is running ( racing) and paddling a ski( racing) roughly the same in terms of difficulty. Never having been a runner ( bum leg) I often wonder if 10k paddling (race) is more or less the same as 10k running (race). I know running burns more calories for the same distance ie: bigger and more muscles involved, but in terms of perceived effect at the end, level of exhaustion. Does running a marathon and paddling one take the same training effort to compete at roughly the same level? I know it's comparing apples and oranges but I was asked this question the other day and I wasn't sure what to say. My guess was my 20k long slow paddles were something like 12-14k similar paced runs but in reality that is just a wild guess and I have no idea. Any thoughts on this?

Bill

Some scattered thoughts:

* Using more muscle mass means you can burn more calories per time unit. I don't think it necessarily means burning more calories per distance.

* From elemntary physics we know that the number of calories required to travel a distance is given by

Energy = (Force of resistance)*(distance)/(efficiency)

A not very good runner (like me) can maintain a speed of about 10 km/h for long distances. An elite marathon runner can maintain about 20 km/h, or about twice as much. A paddler who is about as good a paddler as I'm a runner can also maintain about 10 km/h during long dictances, but not even an elite paddler can maintain anything near 20 km/h for anything longer than very short sprints. IOW, the speed difference between "normal" people and the elite is much larger for runners than for paddlers. From this I conclude that resistance grows faster as a funcion of speed for paddling than for running. That means that while at slow speeds, paddling may require fewer calories per distance, at higher speeds paddling probably requires more instead.

This also means that if normal people taking part in marathons and paddle/run as fast as they can, they will need about as much time, no matter whether they are running or paddling. But for elite guys, a paddling a marathon will take more time than running a marathon.

Some thoughtful conclusions there, Erik. I agree with "more rapid increase in effort vs speed" for paddling vs running.
There are so many variables for this that you would have to ask a more precise question in order to get anything like a useful, or vaguely correct, answer.
I am a runner who paddles. I am better than average as a runner and worse than average as a paddler. This has to do with physique and with with the focus of my training. My speed for any distance (I'll have to extrapolate, because I've never paddled further than 20k and I run mountain ultras) is definitively faster when running. This is despite my heart rate being definitively higher, again for any speed. Hence I am using more calories when running. My perceived effort however, is higher when paddling, because my paddling muscles aren't as strong. With paddling, my limitation is muscular exhaustion, with running, it is cardiovascular, or metabolic, or bloody sore feet.
So within the limits of speed, as described by Erik, I think there will be a variability amongst people dependent on physique and training. However, given the running muscles are larger and more naturally trainable (I don't think the core muscles we use for paddling can be persuaded to change much to fast twitch) I reckon most people would be like me, ie, more easily able to run faster than they paddle, but use more calories doing it.

Interesting question. I often think of a similar question with two of my favourite events, both of which are about the same length of time for me. The Hawkesbury Canoe Classic (101km flat water overnight paddle) and Ironman triathlon (3.8k swim, 180k bike, 42k run) have both taken under 11 hours to complete. Probably both reasonable times, but not setting he world alight. I'd agree with the comments above. People often ask me which is harder, and I always struggle to answer.

I find triathlon/running is mostly an aerobic grind. How hard can I push myself. My heart rate would be higher throughout. The marathon segment is pretty tough on my body, making the post race recovery much longer.

In the paddle, my heart rate is never as high, but my core, back, and shoulders get heavily fatigued. The mental challenge is to not only keep pushing, but hold form and concentration. If I get fatigued, over-caffeinated, or lose concentration while paddling, I fall in (like this year's Hawkesbury). I also admit I am an intermediate paddler in an elite ski for this event.

Which one is harder? I probably find the Hawkesbury mentally harder and ironman physically harder. As an ageing endurance athlete 50 years of age, the hardest part of all is getting to the start line healthy. I had to give up Ironman several years ago due to dodgy knees and have missed several other endurance races due to injuries during training.

Not running but a comparison in cycling/paddling just over the last few weeks for me, a paddling time trial which took 31 minutes and which I'm trained for and a cycling time trial which took 21 minutes and I'm not trained for (mainly been doing low intensity recently) had the same average heart rate (by 1xbeat) and same max heartrate (12 beats off max), both time trials I was doing my best, however I got mean lung burn/tasted blood during the cycle time trial that I have not experienced in years, despite often reaching max heart rate when paddle racing.

The paddle race I was mid pack in results, the cycle race I was in the top third of the results.

Add this into the equation.... Or not.

This is the only reference I have ever see to energy expenditure ( in METS) for racing or hi energy kayaking from actual studies. . The 5 METS referenced always seem more like you average touring pace. It's from this paper.

files.meetup.com/268859/Calories_burned_while_kayaking.pdf

"Above, I gave you a value of 5 METS for energy expended while kayaking. My guess is that the competitor is achieving twice that amount during a race. How do I figure this? I based it on the only 2 studies I know that actually measured energy expended (via oxygen uptake measures) during steady state paddling in experienced/elite kayakers. The first study (Gray et al, Int. J. Sports Med., 1995) measured energy expenditure directly while elite kayakers paddled in the water at a steady state pace. These guys averaged 83.9 kg in body mass and exerted an effort requiring approximately 12 METS. The second study (Bishop, Int. J. Sports Med., 2004), measured oxygen uptake in experienced kayakers while paddling on an ergometer at a pace set at lactate threshold. Lactate threshold, in a nutshell, is right about where a long distance competitor would be, intensity-wise. The athletes in this study weighed 72.2 kg and paddled at an intensity of approximately 11 METS."

Here is another reference to METS and kayaking with comparisons to other activities.

onlinelibrary.wiley.com/store/10.1002/cl...759c33a609478621c0df

Not sure how I feel about the list above. Personally I find it a lot easer to peddle my bike at 25 kph than paddle at 12.5 kph for an hour and I'm in much better paddling shape than cycling. But It's energy expenditure and not perceived effort so that makes some sense. Still, there seems to be some discrepancy in METS between the two references above.

Hmm.. Try this link.

onlinelibrary.wiley.com/store/10.1002/cl...c32bff341ac0c2fcf5b9

Didn't read through the above papers but 25kph would only be an easy recovery pace for most half decent cyclists where as 12.5kph paddling a ski would be near max effort for most.