I am beginning to calculate mechanical efficiency for a horse and carriage vs. an automobile.
my dad recently took his contractor down to the horse market. I am just curious, a horse pulling myself a 300 lb man
what is the mechanical efficiency of this horse and carriage compared to say my automobile which gets 33 miles per gallon and is a Hyundai Elantra 2011
To compare the mechanical efficiency of a horse and carriage to your Hyundai Elantra (33 mpg), let’s break this down step by step:
1. Mechanical Efficiency Definition
Mechanical efficiency is the ratio of useful output (work done) to input energy. For a vehicle, it’s how much of the fuel energy gets converted into motion. For a horse, it’s how much of the food energy gets converted into pulling force.
2. Car Efficiency Calculation
Your 2011 Hyundai Elantra gets 33 miles per gallon (mpg).
1 gallon of gasoline contains about 120,000 BTU (British Thermal Units) of energy.
The Elantra likely has a thermal efficiency of 25-30% (only 25-30% of fuel energy converts to motion).
Let’s estimate 28% efficiency for your car.
3. Horse and Carriage Efficiency
A horse consumes about 20,000 kcal/day in food.
1 kcal ≈ 4.184 kJ, so that’s 83,680 kJ/day.
A horse can produce about 1 horsepower (hp) for a short time or sustain 0.5 hp (373 W) over long periods.
Assuming the horse works for 8 hours a day, that’s about 10,750 kJ of useful work.
The mechanical efficiency of a horse is roughly 10,750 / 83,680 ≈ 12.8%.
4. Comparison
Hyundai Elantra Efficiency: ~28%
Horse & Carriage Efficiency: ~12.8%
Your car is about 2.2 times more efficient than a horse at converting fuel (gasoline vs. food) into mechanical work.
Would you like a more detailed analysis or specific horsepower calculations for your weight and terrain?
You said:
I think the calculation is wrong. How much energy does it take for my horse to go 30 miles, vs my car 30 miles
You’re absolutely right to ask for a more precise calculation. Let’s determine how much energy it takes for your horse and your car to travel 30 miles.
Step 1: Energy Consumption of Your Car
Your Hyundai Elantra (2011) gets 33 miles per gallon.
1 gallon of gasoline contains 120,000 BTU (British Thermal Units), which is 126.1 MJ (megajoules).
So, the energy required for 30 miles:
30 miles /33 mpg = 126.1 MJ ≈ 114.7 MJ
Thus, your car requires 114.7 MJ of gasoline energy to travel 30 miles.
Step 2: Energy Consumption of Your Horse
A horse walking at a moderate speed (~3.5 mph) uses 6.5 MJ per hour.
A horse pulling a cart will likely consume double that due to extra effort, so about 13 MJ per hour.
At 3.5 mph, it takes 8.6 hours to travel 30 miles.
Total energy required:
8.6 hours × 13 MJ/hour = 112 MJ
Thus, your horse requires 112 MJ of food energy to travel 30 miles.
Conclusion: Car vs. Horse
Vehicle Energy Required (MJ)
Hyundai Elantra (2011) 114.7 MJ (gasoline)
Horse & Carriage 112 MJ (food energy)
Surprisingly, the energy required is very close! However, the difference comes from mechanical efficiency:
Your car is about 28% efficient (so 32 MJ of actual work goes into motion, the rest is lost as heat).
A horse is about 12.8% efficient (so only 14.3 MJ of useful work goes into pulling the carriage).
Even though the total energy consumption is similar, the car delivers more work per unit of energy consumed due to its higher efficiency.
Would you like to refine this for different speeds or terrain conditions?
okay fuel costs $3.10 a gallon of fuel, how much does does 112 MJ of hay cost? or at least give me a volume size
Great question! Let’s break down the cost and volume of hay required for 112 MJ of energy.
Step 1: Cost of Fuel for the Car
Your car requires 114.7 MJ for 30 miles.
This is equivalent to 30/33 = 0.91 gallons of gasoline.
At $3.10 per gallon, the fuel cost is:
0.91×3.10= $2.82
So, your Hyundai Elantra costs $2.82 in fuel to travel 30 miles.
Step 2: Energy Content of Hay
Hay has an average energy density of 7.5 MJ per kg (megajoules per kilogram).
To get 112 MJ, we need:
112/7.5 = 14.93kg of hay
That means your horse needs about 15 kg (33 lbs) of hay for this journey.
Step 3: Volume of Hay
Hay has a density of 80-120 kg per cubic meter (depending on compression).
Taking an average of 100 kg/m³, the volume required is:
15/ 100 = 0.15 m^3 = 150 liters
100/15 =0.15 m^3 =150 liters
That’s about the size of a large bale of hay (roughly 5 cubic feet).
Step 4: Cost of Hay
Hay costs $150–$250 per ton (1000 kg), so $0.15–$0.25 per kg.
For 15 kg, the cost is:
15 × 0.20 = $3.00
So, feeding your horse costs about $3.00 per 30 miles—almost the same as your car!
Final Comparison
Vehicle Energy Required (MJ) Cost per 30 miles
Hyundai Elantra 114.7 MJ (gasoline) $2.82
Horse & Carriage 112 MJ (hay) $3.00
Verdict:
Cost per mile is nearly identical (~10 cents per mile).
The car is faster and more efficient but burns fossil fuels.
The horse is slower and less efficient, but runs on renewable energy (hay).
Would you like to factor in horse maintenance costs or fuel efficiency changes with load/terrain?
