the costs of stop and go as well as spinning

If you are ever thinking about buying a rowing machine, we should talk.  I spend something north of six hours a week on one and have come to learn a fair amount about various approaches.   My main machine is a classic Concept II model B that was probably made in 1986.  It was the second generation of the first simulators that were good enough for serious rowing athletes to train on and you can learn a bit of good technique with them.  It is also built extremely well.  You pull a handle attached to a chain that spins a racketed sprocket that is, in turn, attached to a flywheel with some turbine blades cut into its face.  Most of your work goes into swirling the air.  The immediate vicinity of the machine is mostly dust free as a result.

 

This year I added a second machine as something of a splurge.  Nice as the model B is, and there are several newer models but it seems unlikely this one will wear out in my lifetime,  it doesn't go far enough to reproducing the motion of a rower in a shell and you miss some important bits of form as a result.  Most important is the fact that your feet are stationary and your trunk moves back and forth.  Some serious rowing enthusiasts mount their machines on nearly frictionless sliding rails.  Doing this sort of works, but is expensive and takes a lot of room.

 

The folks who make the Concept II machines (they also built most of the racing oars used in competition), came up with a newer design with a clever mechanical system that allows your butt to stay mostly fixed and more closely encourages proper technique.  I splurged and bought one. Lovely and recommended if you intend to also use a proper rowing shell, but more complex and expensive with no real exercise benefit.

 

Why I mention it is that it has a similar flywheel, but adds a shroud with louvers that allow you to control the amount of air the blades can swirl.  This allows you to carefully tailor your training load.  When wide open the air drag is much greater than what the model B produces - as you stop rowing the flywheel comes to a stop much faster than the old design.  One thing you notice right away is that if your strokes are poorly timed or of unequal effort, you end up wasting a good deal of energy.  While this may be ok for exercise, it would be deadly when you are  racing.  There are advantages to a constant speed.

 

Which takes us to the bicycle track.  If you watched the indoor track bike racing event at the Olympics you many have wondered why the riders often travel very slowly and then suddenly burst into wild acceleration as they race to the finish.  You also may have wondered about the unusual disk wheels in some of the events. 

 

It turns out indoor racing is in still air which makes covered wheels practical (no side winds). Smooth wheels have less air resistance than their spoked cousins and  they have a lower moment of inertia than a spoked wheel which gives them a great advantage when accelerating.  

 

When you are riding a bike you have to supply some work to get it up to speed.  Once it is moving there are a couple of forces that try to slow you down - one is friction against the road and the other is air resistance.  At bicyclish speeds the road friction is pretty low - particularly if you are using extremely narrow high pressure track bike tires and pales in comparison to air resistance.  If you stop pedaling and just coast on level ground, you slow and eventually come to a rest.   You can also supply some work to counteract the air resistance (and road friction) and move along at a constant speed.  Most of us have experienced both of these techniques on bicycles (it happens to anything that moves in a fluid, but I happen to love examples that you feel with your own physical exertion).

 

strap in - time for a deeper look

 

To set this up let's look at the energy required to get up to some speed, let's call that v.  Let's call the mass m - in the case of a bike it would be the rider plus her bike, for a runner it is just the person.  You start out with no kinetic energy and end up with E_k = mv²/2.  When you stop you lose all of that energy - mostly in the form of heat.¹  The rate of energy loss (technically power) is just E_k/t, where t is the time it takes to stop.  

 

Let's look at the case where you travel some distance d at a constant speed v and then quickly stop.  You can talk about the average energy loss for that distance as well as the average power loss.  It is just E_k divided by d/v  (d/v is the time it takes to go the distance at a constant velocity).  Substituting you get mv³/2d.  A couple of things to look at ...  this is large when the distance is small and it also grows rapidly with velocity.  So far so good...

 

The other drain is air resistance.  A runner (you can do this for anything moving through a fluid) presents an area towards the wind - let's call that A, and over some time t it sweeps out a volume of air that is just A times the distance she travels or Avt.²  You are pushing a mass of air in front of you away.  The mass is just the density of the air times its volume or m_air = pAvt where p is the density of air (about 1.3 kg/m³ at sea level and average air pressure). ³  When you move through the air the energy you have to supply just moves and swirls the air.  It is just m_airv²/2 or pAtv³/2. Divide by t to get the average rate and t drops out leaving you with pAv³/2.

 

Now it is time to compare the rate of energy loss from braking to the energy loss from air resistance. The ratio is useful:  m/pAd.   If the mass of the runner or vehicle is greater than the mass of the air in the volume tracked out, more energy is lost to braking rather than air resistance.  Another way of looking at it is if this ratio is greater than 1.0 more energy is lost in braking than is spent overcoming air resistance at speed.

 

This is significant.  It tells us when starting and stopping doesn't make sense and can even tell you when an aerodynamic car or bike makes more sense than one that is light weight.  The threshold is just 1 = m/pAd or d = m/pA.  (Note I'm ignoring regenerative braking .. spinning up a generator to stop and storing the energy in a battery, flywheel or capacitor to throw towards starting.  If you know the total conversion efficiency you can just plug it in .. it effectively increases the distances).

 

Plugging in a few numbers you get d ~ 120 meters for a runner, 250 m for a cyclist, and 1,100m for the car.⁴  A useful result.  If you drive with lots of stops and starts it makes sense to get a light weight car and not worry so much about aerodynamics.  If you have a lot of highway driving the weight is not as important as aerodynamics.  Also a cyclist or runner who can easily accelerate (say they are lighter or have more white muscle) can fatigue the competition by setting pace and varying their speed.   

 

Drat - I'm ten minutes over my allotted hour and there isn't time to talk about the inertia in bike wheels.  I'll stop here and pick up there soon.  It adds a bit of complexity, but is quite beautiful and the general concept applies to figure skating, gymnastics, diving and even volleyball.

 

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¹ Two points.  There is another form of energy that goes into spinning the wheels if you have a bike, car or some other wheeled transport.  We'll touch on that later, but I want to keep the argument simple at this point.  Also stopping something can go into sound, flexing a muscle and so on ... but heat is usually the largest sink. 

² A point I'm glossing over.  Here "A" is an effective area that takes into account how aerodynamic the moving body is.  It is the product of a coefficient of drag, a measurable quantity that varies for different shapes - a jetliner or sailplane has a much lower drag coefficient than a runner, bike rider, brick or piano.  So when I say A, I really mean aC_d, where C_d is the drag coefficient and a is the measured cross sectional area you present to the air.  Likewise I should point out that v is the relative air velocity when you are talking about air resistance and the velocity relative to the ground where you are talking about the runner's, biker's or car's kinetic energy.  So we'll just assume there is a perfect calm to keep the equations simple.

³ Rather than track down the html for the greek letter rho, I'll just use p which sort of looks like a rho:-)

⁴ I assume the runner has a mass of 70kg and an effective area A (aC_d) of 0.45m², the rider plus bike has a mass of 80kg and an effective area of 0.25m², and the car and driver have a mass of 1,500kg and an effective area of 1m².

 

 

 

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Recipe corner - two quick tricks

 

Dealing with too much bread

We have a lot of bread from a bit of over experimentation and some of it is getting old.  Rather than talk about making something to begin with, here is my favorite thing to do with slightly older bread (it works on fresh bread too) as long as it still has a bit of moisture.  If the bread is getting really dry, put it in a plastic bag, flit in a bit of water and seal the bag.  In a couple of hours it should be in much better shape unless it is really over the hill.

Cut the bread into half inch thick slices, lay them on a baking sheet and brush one side wit a fair amount of olive oil.  I like using a thyme infused olive oil and, lacking that, I just chop a small bit of fresh thyme into some olive oil awhile before brushing it for a similar effect.  But I love thyme so your mileage may vary.

Pop the pan into a 350°F oven for about five minutes until the bread is slightly toasted and browned - the wonderful Maillard reaction browns the bread and creates dozens of fantastic flavor compounds.  Remove the bread and while it is still warm take a peeled clove of garlic and rub each piece of bread with it as hard as you can without crunching the bread to spread some of the garlicy goodness into a few of the cracks.  Have at it and put as much down as your love of garlic dictates.  Let it them to room temperature. 

I bet you can't eat just one:-)  There are so many possibilities for variations on the theme, so have fun!

 

The simplest "ice cream"

Really simple, really good and not bad for your health either.  The kids can make it too.

Take a few bananas and freeze them.  Break them into smaller pieces and put into a food processor with the standard metal blade.  Switch on and let it run a few minutes stopping every now and again to scrape down the sides.  At some point there will be a neat little phase transition of sorts and it will turn into a semi-frozen mass with the consistency of soft ice cream.  At that point just scoop it out and enjoy it or add some flavorings and spin it for another thirty seconds or so.  I really like throwing in some peanut butter and then adding broken bits of semisweet chocolate afterwards along with some crushed nuts.  Adding a few tablespoons of chocolate syrup is good too.

It turns out bananas have a boatload of pectin.  Pectin is concentrated in the walls of the plant cells and the mechanical action of the blades breaks the cell walls and allows the pectin to form into lovely pectin chains which form the basis for the gel that has the nice ice creamy texture.