Some Timely and Time Saving Observations Concerning Gasoline, Solar Power, andHorses (horsepower),Zebras (zebrapower) When doing farming or driving to work!Using conversion factors found in an old hydraulics book, some data on a covert government website and assuming zebras are just horses with a striped attitude, let us establish the conversion between gasoline and horsepower-hours:
Step 1-Establishing Zebra - Gasoline equivalency If you have 100% efficiency and as many books would suggest one gallon is about 140000 Btu/gal, converting you would get about 55 Horsepower-hrs/gallon (this is an optimistic estimate based on U.S. gallon). This means one gallon of gas is the equivalent of: 2 zebra days with one zebra working 24hrs/day for two days at 100% efficiency or a wishful 6 zebra days if zebras would work 8 hrs days and then shut off.... They don't. In truth, we have over estimated because zebras don't stop metabolizing when they are asleep (as per most non-theoretical animals, e.g. crocodiles), they can't work a 24 hour day. And worse, their metabolism is less than 50% efficient so you only get about 1/6 as much work as you would hope. To keep things simple, however we will grant that error and say: 1 gallon of gas is about 55 HP-hours(mechanical) or about 2 zebra days, 55 ZP-hrs hours (actual zebras) based on a 100% efficiency, 24 hour wonder zebra. We can call this the gasoline zebra equivalence. CONCLUSION #1: In truth, you only get about 10 ZP (Zebra-Power)-hours per day per zebra :( But a gallon of gas is worth 55 zebra-hours, a lot of zebra hours! Factoid: Zebras have been used to farm in Africa because of their immunity to disease. =============================================================================== Step 2. Dispelling the myth of the 300 mile per gallon car (LOL). This is a matter of calculating force times distance to find the energy consumed or the force times velocity to calculate power! Assume a car has a 5ft x 5ft profile pushing the wall of air in front of it to 55 mph, we can calculate the approximate zebra power needed to do this based on pressure and velocity using
Bernoulli's formula with appropriate conversion factors as a first approximation (see wikipedia etc.):
P/(0.433*ϒ)=v^2/2g P=pressure in psi, v=velocity in ft/sec, g=acceleration of gravity in ft/sec^2, about 32.2ft/sec^2. My wife would laugh, I couldn't remember the approx. molecular mass of air so I used nitrogen (close at 28). This means the approx. density(ϒ) of air at STP (Standard Temperature and Pressure) is, in gm/cc, 28gms/22400cc=0.00125gm/cc Next convert speed to ft/sec using the factor label system: v=55mi/hr*(hr/3600sec)*(5280ft/mi)=80.66ft/sec Therefore, completing the Bernoulli calculation, the pressure roughly would be: p=.433*.00125*80.66*80.66/(64.4)=0.0546 lb/in2 Since we know the pressure and the area we can estimate the force. Or, if you want to do this right, hire Arnold Shwarzenegger to hold a bathroom scale and a 5'x5' piece of plywood out the window of your car! Using Pascal's formula: F=P*A= (.0546*60*60) ≈ 196 lbs of force on that 5'x5' piece of plywood (Thanks Arnold!) Knowing the force and the speed we can now estimate thehorsepowerzebrapower: ZP=(lbs*Vft/sec)/550=196*80.66/550=28.74 ZP At one hundred percent efficiency, traveling 55 mph would take 28.74 ZP (roughly 30 zebras if you could actually get them in your car). Total hours for one gallon of gas at about 55 hp-hrs/gal is estimated as 55/28.74=1.91hrs or
105 miles if traveling at 55 mph. CONCLUSION #2: With 100% maximum mechanical efficiency you only get about 105 mpg at 55 mph, and this does not include road friction which increases with weight and tire compliance. Note: one delightful conclusion: sneaky idea... %efficiency is roughly equal to miles/gallon
Funny part here, antigravity, levitation, all that stuff WON"T HELP and DOESN'T REALLY MATTER!! Hence, unless you reduce your wind profile, the best you will ever get for mileage at 55mph is about 105 miles/gal..=============================================================== I used to drive about 25 miles to work at about 55 mph. This same trip using a striped horse and avoiding crocodiles at 3-4mph would take about 8hrs. Then assuming I drove home the next day that would be another 8hrs. Since I actually take about 10 such trips per week for 10 gallons of fuel I'm not doing too bad even though I'm only getting 25 mpg (25% efficiency). (and my non-striped Chevy isn't tired, or drinking gasoline at night, or eaten by crocodiles, and I get some work done, I'm not on the road 16 hours/day, plus I don't get those pesky saddle- sores from riding all day, whew)!! To be honest, you would have to swap ponies like the old west. Restating our original analysis then, one gallon of gas gives me the use of about two good domesticated zebras for about one very long troublesome crocolicious day, about 50 ZP-hours!! I hate zebras already. How bad Would it smell? =====Eez Reel News Bureau file photo =============== Factoid: Many Amish farmers, like former President Bush shown on his ranch in Crawford, Texas shown below, have plowing teams of 6 to 10 animals (horsepower).Step 3- Dispelling the myth of solar powered tractors and going back to horses for farming Now comes the fun part, suppose I want to do farming with old stripey dobbin but my neighbor convinces me to use solar power because of his sensitivity to Z vapors. Sunlight provides about 1kw/m^2 but with a solar array of ten percent efficiency I only get 100W. To get the utility of one zebrapower I need 746 watts or translating this into solar panels I need about 8 square meters (about 6ftx12ft). CONCLUSION #3: 8 square meters of solar panel could deliver one Zebra Power, 1 HP. So I would need 80 square meters to build a solar powered tractor equivalent to an Amish bridle of 10 Horses..... Imagine, you go to the store and get a hydraulic pump, a gear reducer, a battery, a big electric motor, a titanium trailer, a bunch of hoses, valves, etc. You weld up a 3 point hitch and a single point plow and I go for it. You mount roughly 40 200Watt solar panels (80 square meters). So now maybe I double my solar array and I am starting to look like a caterpillar going across the field, but the field is eventually plowed! (clean the dust off the panels please! Here is another calculation: 1000 lbs of force moving at 10ft/sec/550=18 HPor ZP equivalents. That's a lot of striped beasties or a whole caravan (18x8 or 144 square meters) of pretty expensive solar panels, i.e. roughly 72 of the darn things.
Most small tractors are 24-40 HP, Most Amish go smaller with say 10 horses, but the penalty is time So, yes we can save gasolene vapors but we're going to need weeks to plant our fields, pretty much like the Amish. Maybe if we add AI and a GPS tracker computer for a zillion$ to guide the whole thing so we won't have to sunburn ourselves quite. Or maybe we can charge the batteries from a panel array, this works but you don't want to figure the size of the battery, huge & dangerous! Consider the following estimates of farm HP-hrs to till a field, horses or zebras it's all the same! ( From: http://www.ext.colostate.edu/PUBS/FARMMGT/05006.html). With 24 hp-hrs to plow one acre (at 100% eff.), 100 acres would take between 50 and 200 gal of gas and up to 100 hours. Our solar contraption might need 600 hours, roughly 100 days!! For heaven sakes that must be wrong! To plow 8" deep with 25% efficiency, my 3HP rototiller for example will do 1/16 acre in 2 hours (32hrs/acre) or 100 HP-HRS/acre at about 8 gallons of gas/acre (hmm, lovely!!! 4 times as much as a regular tractor at 2 gallons/acre). Who knew Colorado State might actually know their stuff?!! And it looks like I may need to tune up my old rototiller engine (But I already knew that!). ================================================================================== As was just so miraculously discovered, Like driving where you don't get 105 mi/gal, you also don't get 100% efficiency in plowing either. If you want to know why hamburgers became so popular in this country try spending the next 100 days behind a zebra, or 25 days behind 4 zebras!! Cows and grazing animals can save our farmers and farmgodesses a lot of work and a lot of wear and tear on old Dobbin and friend!! Any body jewelry, however, that you apply to your zebra, ear rings, eyelid piecings, etc. no matter how beautifully hand crafted, after 100 days they just fall off on the ground, causing the "anything zebra" avaricious crocodiles to eat the jewelry, and this could drive up your bill and require prompt crocodile veterinary attention.. Unfortunately, this is the third ear ring they've eaten this week...... Our next installment: "The Chronic Need for New Reptile Veterinary Students" or "Talking your Zebra out of the need for body jewelry".
Operation Energy-use rate, PTO hp-hrs/acre Gallons per acre Gasoline Diesel LP gas Shred stalks 10.5 1.00 0.72 1.20 Plow 8 inches deep 24.4 2.35 1.68 2.82 Heavy offset disk 13.8 1.33 0.95 1.60 Chisel plow 16.0 1.54 1.10 1.85 Tandem disk, stalks 6.0 0.63 0.45 0.76 Tandem disk, chiseled 7.2 0.77 0.55 0.92 Tandem disk, plowed 9.4 0.91 0.65 1.09 Field cultivate 8.0 0.84 0.60 1.01 Spring-tooth harrow 5.2 0.56 0.40 0.67 Spike-tooth harrow 3.4 0.42 0.30 0.50 Mulch treader 4.0 0.42 0.30 0.50 Rod weeder 4.0 0.42 0.30 0.50 Sweep plow 8.7 0.84 0.60 1.01 Cultivate row Crops 6.0 0.63 0.45 0.76 Rolling cultivator 3.9 0.49 0.35 0.59 Rotary hoe 2.8 0.35 0.25 0.42 Anhydrous applicator 9.4 0.91 0.65 1.09 Planting row Crops 6.7 0.70 0.50 0.84 No-till planter 3.9 0.49 0.35 0.59 Till plant (with sweep) 4.5 0.56 0.40 0.67 Grain drill 4.7 0.49 0.35 0.59 Combine, small grains 11.0 1.40 1.00 1.68 Combine, beans 12.0 1.54 1.10 1.85 Combine, corn and grain sorghum 17.6 2.24 1.60 2.69 Corn picker 12.6 1.61 1.15 1.93 Mower (cutterbar) 3.5 0.49 0.35 0.59 Mower conditioner 7.2 0.84 0.60 1.01 Swather 6.6 0.77 0.55 0.92 Rake, single 2.5 0.35 0.25 0.42 Rake, tandem 1.5 0.21 0.15 0.25 Baler 5.0 0.63 0.45 0.76 Stack wagon 6.0 0.70 0.50 0.84 Sprayer 1.0 0.14 0.10 0.17 Rotary mower 9.6 1.12 0.80 1.34 Haul small grains 6.0 0.84 0.60 1.01 Grain drying 84.0 8.40 6.0 10.08 Forage harvester, green forage 12.4 1.33 0.95 1.60 Forage harvester, haylage 16.3 1.75 1.25 2.10 Forage harvester, corn silage 46.7 5.04 3.60 6.05 Forage blower, green forage 4.6 0.49 0.35 0.59 Forage blower, haylage 8.3 0.35 0.25 0.42 Forage blower, corn silage 18.2 1.96 1.40 2.35 Forage blower, high-moisture ear corn 5.9 0.63 0.45 0.76 Step 4- Interconverting
CONCLUSION #4: There is an obvious trade off between time and horsepower. You can now do the math. Take any of the tasks above and multiply the gas usage by 55. This gives you the actual horsepower hours. Now, you can either up the hours or up the horsepower (or actual horses/zebras) to achieve that task. Note if you take that middle column, hp-hours, this would seem to equal the number of horses (or zebras) times the number of hours so you could plow but unfortunately this is at the PTO (power take off) after a slew of inefficiencies, so you would have to multiply estimates by up to maybe 5.>>>> 1 acre in five hour with 24 horses, or 1 acre in 20 hours with 6 horses, or 1 acre in fifteen days with one horse!!! etc. The point is it takes a lot of hungry furry beasts. The alternative is to not plow so deep or to not use furry beasts at all. Imagine now your typical grain farmer doing 5000 acres. Either he has a very large extended family or he uses gasoline!! Now read the book, "The Winter Harvest Handbook" and think... then think some more, then go back thru all these calculations. Why would I recommend a book on organic gardening, because of the zebras!!
