Final answer:
The theoretical capacity of a 2-row cotton harvester traveling at 3 miles per hour is 6.6 bales per hour. With a field efficiency of 55%, the effective field capacity is 3.63 bales per hour.
Step-by-step explanation:
To calculate the theoretical capacity in bales per hour of a 2-row cotton harvester, we use the given information that the field yields 1.5 bales per acre and the harvester travels at 3 miles per hour. We begin by converting the harvester's speed to acres per hour. Since the rows are 40 inches apart, we have:
- There are 12 rows of cotton in 1 acre (since 40 inches is approximately 1/3 of a yard, and there are 4840 square yards in an acre).
- Each row is 3 miles long (since the harvester travels 3 miles per hour).
- So, 3 miles is equivalent to 3 * 5280 feet per hour (since there are 5280 feet in a mile).
- The harvester covers 2 rows at a time. Thus, it covers 2 * 3 * 5280 feet of row per hour.
- That makes 2 * 3* 5280 / 3 (to convert to yard units since 3 feet is 1 yard) feet of row per acre.
- This equals 6 * 5280 / 3 square yards per acre each hour.
To get the theoretical capacity, we multiply the number of acres it can cover per hour by the yield per acre:
- 2 * 3 * 5280 / 4840 bales per hour
- Which simplifies to 2 * 3.3 bales per hour.
- The theoretical capacity is thus 6.6 bales per hour.
However, because the field efficiency is only 55%, the effective field capacity in bales per hour would be:
- 6.6 bales per hour * 0.55
- Which results in 3.63 bales per hour as the effective field capacity.