Exploring cost of transport

Question

Potentially useful information:

1 mile = 1609m

1 gram of H2O = 1 ml H2O

Energy content of fat is 39.3 kJ/gram and 2.0 L of O2 is consumed per gram of fat metabolized

Kinetic energy = ½ mv2, work = F X D

gravitational potential energy = mgh,

g = 9.8 m/s2

RER= CO2 produced per unit time/O2 consumed per unit time

Efficiency=work out/energy in=25% for muscles

Weight-specific cost of transport for walkers/runners= 8.46 M-0.40 (where mass is entered as grams, and is expressed in units of mLO2 per gram of body tissue per kilometer)

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In 2007, a group of researchers recreated Vance Tucker’s groundbreaking 1968 parakeet experiments using cockatiels (Nymphicus hollandicus )1. Examine the curve below which is a measurement of the energy cost of flight in a 80.5 gram bird across several speeds

1) What is the minimum cost of transport in this bird? (make sure you include appropriate units in your answer) Please report in total (whole animal) cost of transport

Potentially useful information:

1 mile = 1609m

1 gram of H2O = 1 ml H2O

Energy content of fat is 39.3 kJ/gram and 2.0 L of O2 is consumed per gram of fat metabolized

Kinetic energy = ½ mv2, work = F X D

gravitational potential energy = mgh,

g = 9.8 m/s2

RER= CO2 produced per unit time/O2 consumed per unit time

Efficiency=work out/energy in=25% for muscles

Weight-specific cost of transport for walkers/runners= 8.46 M-0.40 (where mass is entered as grams, and is expressed in units of mLO2 per gram of body tissue per kilometer)

__________________________________________________________________________________

In 2007, a group of researchers recreated Vance Tucker’s groundbreaking 1968 parakeet experiments using cockatiels (Nymphicus hollandicus )1. Examine the curve below which is a measurement of the energy cost of flight in a 80.5 gram bird across several speeds

1) What is the minimum cost of transport in this bird? (make sure you include appropriate units in your answer) Please report in total (whole animal) cost of transport

Speed (m/s) VO2 (mLO2/kg·s)

5 7.7

6 7.2

8 5.4

10 5.1

12 6.3

14 6.6

15 8.3

2) If this bird has fat reserves of 3 grams (which is only about 4% of its body weight), how many miles can it fly using only its fat reserves?

3) How many joules of heat (min) will it produce?

4) If the fat is triglycerides, then a reasonable chemical formula is C51H140O6. Using only this fat, what will is the Respiratory Exchange Ratio (RER) of the bird when it is flying?

5) How many L of CO2 will it produce during its flight? (hint – again, be careful about units!)

6. Finally, compare the weight specific cost of transport between this cockatiel and a walker/runner of similar mass (e.g. something like a chipmunk). BY WHAT FACTOR (I.e. how many times) is the walker/runner cost of transport larger than that of the flier (the cockatiel)? It’s a lot energetically cheaper to fly!

Answer 1

Exploring the Cost of Transport

Step 1: Minimum cost of transport

The bird’s oxygen consumption is lowest at 10 m/s where VO₂ = 5.1 mL O₂ / kg·s.

Convert this to a whole-animal rate:

Vdot_O2,bird = 5.1 mL O₂ / kg·s × 0.0805 kg = 0.411 mL O₂ / s

To express as cost of transport (mL O₂ per m body mass):

COT = 0.411(0.0805)(10) = 0.51 mL O₂·g⁻¹·km⁻¹

So the minimum cost of transport ≈ 0.51 mL O₂ · g⁻¹ · km⁻¹, or about 41 mL O₂ per km for the entire 80.5 g bird.

Step 2: Range using 3 g of fat

Energy from 3 g fat:

3 g × 39.3 kJ/g = 118 kJ

Each g fat → 2.0 L O₂ consumed → 3 g → 6 L O₂ available.

O₂ cost per km ≈ 0.041 L, so

6L / 0.041 L km⁻¹ ≈ 146 km

That’s roughly 90 miles of flight on 3 g of fat.

Step 3: Heat production

Muscle efficiency = 25%, so 75% becomes heat:

118 kJ × 0.75 = 88.5 kJ of heat

If the flight lasts 146 km / 10 m s⁻¹ ≈ 14 600 s (≈ 244 min):

88.5 kJ / 244 min ≈ 363 J min⁻¹ heat

Step 4: Respiratory Exchange Ratio (RER)

For triglyceride C₅₁H₁₄₀O₆:

C₅₁H₁₄₀O₆ + 72.5 O₂ → 51 CO₂ + 70 H₂O

RER = 51 / 72.5 ≈ 0.70, typical of pure fat metabolism.

Step 5: Total CO₂ produced

6 L O₂ × 0.70 = 4.2 L CO₂ produced over the full flight.

Step 6: Compare to a walker/runner (chipmunk-sized)

Weight-specific COT (walkers/runners):

8.46M^(−0.40) = 8.46(80.5)^(−0.40) ≈ 1.65mL O₂·g⁻¹·km⁻¹

Bird’s COT ≈ 0.51 mL O₂·g⁻¹·km⁻¹.

Factor = 1.65/0.51 ≈ 3.2

So walking/running costs about 3× more energy than flying for the same-mass animal.

Summary

1. Minimum COT: 0.51 mL O₂ · g⁻¹ · km⁻¹ (≈ 41 mL O₂/km whole-animal)
2. Range on 3 g fat: ~90 miles
3. Heat output: ≈ 360 J min⁻¹
4. RER: 0.70
5. CO₂ produced: 4.2 L
6. Walker vs Flier cost: ≈ 3× higher for walker