[workbike] PIGS (long)

PIGS might be thought of as an anacronym for "Power is 
a Grand Subject".

The question of whether or not moving 300 lbs of cargo
over 20 hilly miles can be done has been answered by 
history. We have tons of examples of even greater feats 
such the Egyptian's moving massive stone blocks many miles. 
The same exhibition of mind, muscle and inguenuity occured 
at Easter Island, Stonehedge and countless other places;
like rural China were HPV transport of heavy agricultural
products is still somewhat common place.

If it were a just a matter of thinking about moving
300 lbs 20 miles the WORK accomplished would represent 
31,680,000 ft-lbs of energy. Fortunately dragging 
something along usually involves less pulling force 
to overcome friction than the weight of the object 
being moved. A good set of ball bearings and low
rolling resistance tires, as provided by a quality
trailer or cart, can push the pulling force down,
way down. On the flats if dealing with a realistic 
Coefficient of friction of 0.02 the pull force would 
sink to 6 lbs, thus the WORK involved to accomplish 
the chore would also magnificently decrease to 
633,600 ft-lbs.

Work is distance times force.

We modern bipedal apes seem to be fixated on the 
notion of time. How much time is involved with performing 
a certain amount of WORK is POWER,  e.g., the rate of WORK.

Power is Work per time.

The faster Work occurs the greater the amount of Power needed. The 
slower Work occurs the lower the amount of Power needed.

If we were to cycle pell mell pulling a trailer, with a Crr 0.02, 
carrying those 3 little pigs 20 miles in one hour (over level 
ground and discounting other sources of drag) the Power required 
would be Work/Time: 633,600 ft-lbs/3,600 seconds = 176 ft-lbs/sec
or 0.32 horsepower.  That's approaching the limits of what 
a fit cyclist can perform in one hour!

By slowing down the rush to a more reasonable Earth and 
human-scaled pace, say 5 mph, thus increasing the pig puller's 
work shift to four total hours, the Power required would 
become: 633,600 ft-lbs/14,400 seconds = 44 ft-lbs/sec or 0.08 hp 
(about 60 watts).

Briefly expressed, the formulation to determine the power 
needed to overcome rolling resistance is: 

Power = mass x coefficient of rolling resistance x velocity

The unit of measure HUP stands for human power, as contrasted 
cleverly to horsepower. 1 hup equals the power an average 
human can sustain for 8 hours before collapsing into sweaty
pile of fatigue. Roughly 1 hup represents the same power
as 0.1 hp or in common metric units 75 watts.

Obviously there are other mysterious forces of the universe
clutching at every workbiker, desparately trying to toss us 
into the dark pit of entropy. Gravity is weighty subject.
While climbing hills we ponder it's existance the same way
we might regard a mosquito buzzing in one ear. Why hath God
wrought this vile bain? As with most things in life, vile
bains or devine gifts exist by virtue of our own free 
will, the result of choice and attitude. 

On a smooth level stretch of road, gravity's effect while
pulling the pigs to market has been defined solely by
rolling resistance. When pointing ourselves and Porky and 
friends towards the sky the towing force will increase in 
direct relationship to the slope of any hill we encounter. 

On 5% grades the porkers' mass will be pulling back towards the 
center of the Earth with a force equal to 5% of their weight, in 
this example that's 15 lbs. When pointed downhill, the squealing 
lard and meat will be pushing with a 15 lb force. A 3% grade, 
approx 3% of the towed mass becomes a resisting or additive 
force. Pretty cool relationship, eh? And, one that generally 
holds true for all grades measuring under 10%.

Just as before, the Power of gravity induced drag
can be expressed as relationship involving velocity:

    Power = mass x grade x velocity

I'll scribble it out... carry the one... substract the 3...
tickle the 7...

While ascending a 5% positive grade at 5 mph the pigs' 
mass will stack on an additional 0.2 hp to the 0.08 hp
rolling drag power already accounted for. Bummer, a normal
human could manage less than 5 miles at that rate. 
Fortunately, slowing down by half while climbing, taking 
such a climb at 2.5 mph, the gravity and friction tax also 
drops by half. Specifically to 1.25 hup -- a little higher 
power requirement but still a very comfortable exertion 
level.

And every red-blooded bicyclist knows about evil Lord Air 
Resistance. Can't forget him can we? Oh, yes we can -- almost. 
At walking speeds, air behaves kindly by moving away with 
little complaint. Air has mass, but it's relatively small 
per unit of volume. The lower a cyclist's velocity the
less important air resistance becomes. That's why picket line 
marchers can slowly stomp around in circles with their 
wide-flat signs held high and still have enough energy to 
shout slogans. 

So, what's the CdA of a Piglet in a paceline? I don't rightly 
know. Most likely high. But at 5 or less miles per hour the total 
contribution of 3 thigh-high pigs' aerodynamic drag to the total 
power requirement will be less than 4%. If a big storm blew up, 
air resistance would suddenly become a viable concern. From my 
limited barnyard social experience pigs generally claim to like 
nice weather as much as humans do. Taking them to market on a 
calm day would make a suitable farewell gift.

There's an interesting relationship which exists between
the velocity while climbing, the higher velocities 
experienced while descending, and overall trip speed. In 
retrospect it's logical. In hilly terrain, where the 
distance of the uphill portions might equal the distances 
of the downhill portions the average trip speed can never 
exceed twice the average climbing velocity.

Imagine riding an upright cruiser, grinding up a long steep hill
1 mile in length, and needing 30 grueling minutes to complete 
the ascent. The climbing speed was thus 2 miles per hour. 

Now add to the vision the bike's handlebars being equipped 
with a near-instantious teleporter button. With a click of a 
finger the bike and rider zooms at a rate far exceeding 
the speed-of-light back to the base of the hill. Thus the 
total round trip of 2 miles would have happened after 30 
minutes climbing plus the infinately small quanta of time 
needed to go back down hill. 

Total time ca. 30 minutes. Total distance 2 miles. Average 
velocity of the complete trip almost, but not quite, 4 miles 
per hour! 

Eschewing the mythical teleporter, if the descent were done with a 
cautious application of coaster brakes, say at 12 mph, the downhill 
leg would grow to 5 minutes. Total trip time would then be 35 minutes.
The average speed to realistically cover 2 miles... <tada>  about 
3.5 mph.  A 0.5 mph difference. Significant if one is fighting 
to win the Tour de France. Insignificant if one is performing 
an honorable Salt-of-the-Earth chore.

The point being: in an HPV cargo hauling situation over rolling 
hills there's little incentive or benefit to race downhill.  
Consequently lots of pig provided aero-drag might be regarded as 
a wonderful thing to exploit. Up at 2.5 mph, down at 12 mph. If the 
uphills equal the downhills this roughly implies a sustainable, safe 
4 mph average over 20 miles, at least 5 hours on the road one way, 
much likely less maybe more. This is positively Star-Trekian warp 
speed concidering the alternatives.

I have had the unbidden honor of taking a stroll with a small 
herd of pigs on occassion. They are quick, sly, smart and 
pig-headed. Rarely will a beady-eyed pig proceed in a straight 
line when a zigzag and sarastic grunt will do. Three pigs means 
3 sets of chaotic zigzags. Net forward walking velocity in the 
presence of swirling swine sometimes can be measured in
units of feet per day. A pet trained to walk on a leash 
would be too much of a friend to even bother with the 
journey.

Hiking while carrying the 300 lbs 20 miles might be possible 
for an exceedingly small portion of our species.

Hitch a ride in an auto?  It'll be an option for awhile. 
There are more enjoyable and easier ways of getting about.

To a well-maintained Mountain Bike, hitch a stout quality 
workbike trailer, such as Jim crafts. Load the pigs on, ensuring 
that they can't wander around to upset the Center of Gravity. A 
wire cage might be prudent.  Walk the bike and trailer up steep 
hills. Coasting down at modest speeds will keep the load under 
control and avoid the unneccessary requirement for exotic braking 
systems to deal with elevated Kinetic Energy. Pack two lunches, 
lots of bike tools, some water and shade for the pigs, and 
most important plenty of patience and good thoughts for Mother 
Earth and Father Sky. A cyclecomputer would be a rational accessory 
to help match the velocity to the all day effort, thus providing a 
sideways glance at power which should hover at the 1 hup mark.

The task is doable, a reasonable goal, and responsible.

John Snyder

• Follow-Ups:
  • Re: [workbike] PIGS (long)
    • From: "F.Lenk" <lenkf@vcnet.com>