Question:
Find the annual yield by Von Mantel's formula for a sal forest having total volume 10,000 cubic meter and the rotation age is 100 years.
Find the annual yield by Von Mantel's formula for a sal forest having total volume 10,000 cubic meter and the rotation age is 100 years.
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Von Mantel formula: \(Y = 2V/R\). It is the simplest and most famous formula for yield regulation. Remember the "2" in the numerator!
Updated On: Aug 7, 2026
- 200 cubic meter
- 220 cubic meter
- 20 cubic meter
- 100 cubic meter
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Question:
The question asks to calculate the sustainable annual harvest (yield) of a forest using the classical Von Mantel's formula, which is a simple volume-based method for yield regulation in even-aged forests.
Key Formula or Approach:
Von Mantel's Formula is: \[ Y = \frac{2 \times V}{R} \] Where: - \(Y\) = Annual Yield (the amount to be harvested every year).
- \(V\) = Total growing stock (Volume) of the forest.
- \(R\) = Rotation (the age at harvest).
Step 2: Detailed Explanation:
• Given Data: - Total Volume (\(V\)) = 10,000 cubic meters. - Rotation (\(R\)) = 100 years.
• Calculation: \[ Y = \frac{2 \times 10,000}{100} \] \[ Y = \frac{20,000}{100} \] \[ Y = 200 \text{ cubic meters} \]
• Rationale: Von Mantel's formula assumes the forest has a "normal" distribution of all age classes from 1 to 100 years. In such a perfect forest, the sustainable yield is exactly twice the volume divided by the rotation age.
Step 3: Final Answer:
The annual yield for the sal forest is 200 cubic meters.
The question asks to calculate the sustainable annual harvest (yield) of a forest using the classical Von Mantel's formula, which is a simple volume-based method for yield regulation in even-aged forests.
Key Formula or Approach:
Von Mantel's Formula is: \[ Y = \frac{2 \times V}{R} \] Where: - \(Y\) = Annual Yield (the amount to be harvested every year).
- \(V\) = Total growing stock (Volume) of the forest.
- \(R\) = Rotation (the age at harvest).
Step 2: Detailed Explanation:
• Given Data: - Total Volume (\(V\)) = 10,000 cubic meters. - Rotation (\(R\)) = 100 years.
• Calculation: \[ Y = \frac{2 \times 10,000}{100} \] \[ Y = \frac{20,000}{100} \] \[ Y = 200 \text{ cubic meters} \]
• Rationale: Von Mantel's formula assumes the forest has a "normal" distribution of all age classes from 1 to 100 years. In such a perfect forest, the sustainable yield is exactly twice the volume divided by the rotation age.
Step 3: Final Answer:
The annual yield for the sal forest is 200 cubic meters.
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