1. A truck is coasting along on a flat road at an initial velocity of 50 mph. It eventually comes to a stop. Would the truck have coasted (longer, the same or shorter) if the payload had been 1500 pounds heavier?

2. A hockey player is coasting along on flat ice at an initial velocity of 15 mph. She eventually comes to a stop. Would she have coasted (longer, the same or shorter) if she had weighed 50 pounds more?

3. A kayak is coasting on a flat pond at an initial velocity of 2 knots. It eventually comes to a stop. Would the kayak have coasted (longer, the same or shorter) if it had carried an extra 50 pounds in the hatches?

Note: assume no wind resistance for all three cases.

I'm thinkin' about it, but in the meantime, I like that you made the hockey player a female! :-)

divide Newton's law by the frictional force and mass drops out.

divide Newton's law by the frictional force and mass drops out.

Phil, that’s correct for the hockey player and truck case. That’s because the frictional force is u*m*g for the hockey case.

So we have m*a = - u*m*g, where u is the coefficient of friction of the ice, m and a are the mass and acceleration of the skater, respectively and g is the acceleration of gravity. An analogous expression for the truck case. But what about the kayak case?

-Leon

functional assumption is that the amount of contact area doesn't change the frictional force. Not sure that is a good assumption for boats with the change in wetted area and displacement.

-Phil

[this is what I get for hanging out with engineers all day ;-) ]

A hockey player is paddling a kayak on a truck. Where are they going and why?

A hockey player is paddling a kayak on a truck. Where are they going and why?

Where?:

If Wing then

To closest race

Elseif Euro then

To closest rock garden

Elseif Stick then

To roll

Else

To hand roll

Endif

Why?:

I have no idea. It’s probably a female thing. Perhaps pinkpaddler knows.

1. A truck is coasting along on a flat road at an initial velocity of 50 mph. It eventually comes to a stop. Would the truck have coasted (longer, the same or shorter) if the payload had been 1500 pounds heavier?

2. A hockey player is coasting along on flat ice at an initial velocity of 15 mph. She eventually comes to a stop. Would she have coasted (longer, the same or shorter) if she had weighed 50 pounds more?

3. A kayak is coasting on a flat pond at an initial velocity of 2 knots. It eventually comes to a stop. Would the kayak have coasted (longer, the same or shorter) if it had carried an extra 50 pounds in the hatches?

Note: assume no wind resistance for all three cases.

Time to put some closure to this topic. The answers are:

1. Same

2. Same

3. Shorter

In the first two cases the coast times are independent of the weight of the truck and skater. I showed why this is so in an earlier post.

The third case is different because water is a viscous medium and the kayak’s drag is a function of speed and weight. The more weight you add to a kayak the more it sinks. Accordingly, more water is displaced and the wetted surface area is increased. The frictional drag on a kayak increases with increasing surface area and the wave drag increases with increasing displacement. Although a heavier kayak has more momentum, the additional momentum is countered by the increase in drag (frictional drag + wave drag). Adding weight to a kayak not only increases its resistance to accelerate, but makes it decelerate faster when it coasts (shorter coast). Although beyond the scope of this post I can provide a proof offline.

BTW, that’s why racers want lightweight kayaks. They accelerate faster to get to speed and coast longer between the stroke exit and next power stroke.

Time to put some closure to this topic. The answers are:

1. Same

2. Same

3. Shorter

In the first two cases the coast times are independent of the weight of the truck and skater. I showed why this is so in an earlier post.

The third case is different because water is a viscous medium and the kayak’s drag is a function of speed and weight. The more weight you add to a kayak the more it sinks. Accordingly, more water is displaced and the wetted surface area is increased. The frictional drag on a kayak increases with increasing surface area and the wave drag increases with increasing displacement. Although a heavier kayak has more momentum, the additional momentum is countered by the increase in drag (frictional drag + wave drag). Adding weight to a kayak not only increases its resistance to accelerate, but makes it decelerate faster when it coasts (shorter coast). Although beyond the scope of this post I can provide a proof offline.

BTW, that’s why racers want lightweight kayaks. They accelerate faster to get to speed and coast longer between the stroke exit and next power stroke.

A small mistake led to a big mistake in one of my answers. Ugh, I hate when that happens. Mea maxima culpa! I need to set the record straight. I said that I could prove that “Adding weight to a kayak not only increases its resistance to accelerate, but makes it decelerate faster when it coasts (shorter coast).” The second part is false. My purported proof was based my own home-brew mathematical model of wave resistance. Recently, I found a simple mistake in my model. So, after correcting the mistake, the correct answer becomes:

Adding weight to a kayak makes it decelerate slower (longer coast).

To make sure that I got it right, now, I verified it with John Winter’s KAPER drag prediction program (Sea Kayaker Magazine uses KAPER as one of the programs for performance prediction.). Stupid me, why didn’t I test my model against KAPER originally?

But the important thing still is that, given kayaks that have design displacements reasonably matched to your weight and cargo, lighter kayaks allow you to go farther or faster with no additional time or work. That’s because drag increases as more dead weight is added to the kayak. However, with my corrected conclusion above, there is a small price to pay in momentum with a lighter kayak during the coast between strokes. Nevertheless, the reduced drag from a lighter kayak drowns out the momentum gain from coasting with a heavier kayak. Additionally, the momentum of a heavier kayak becomes a big disadvantage during the power phase of each stroke; that’s because the kayak must accelerate with each stroke and that’s when momentum works against you.

Most NSPN trips are paddled at no more than 4 knots. At that relatively low speed frictional resistance is the main component of drag. With a little simple calculus on the resistance drag equation and some assumptions about how much a kayak sinks as weight is added I came up with an interesting result. For a 1-% increase of weight (the total weight of the boat and its contents), and everything else being equal, there is a 6% loss of speed.

Besides everything else, one problem in buying a kayak is finding one that fits with respect to your weight (a design displacement problem). Most manufacturers don’t provide the design displacement, even for racing/fitness kayaks. For example, after repeated queries to Epic asking for the design displacement for the 18X model, the best they could provide was:

“The 18X Sport has the most volume because it is 18' and slightly wider than the 18X. The 16X has the least volume being shorter, but is the most stable of the 3. Still, all of these boats are designed to perform well all the way from a 120 lb. paddler up to 320+ lbs. of paddler plus gear.”

Wow, quite a range!

-Leon