Subtopic: Functional requirements, principles of working, construction and operation of manual, animal, tractor and renewable energy operated equipment for tillage, sowing, planting, fertilizer application, inter-cultivation, spraying, mowing, chaff cutting, harvesting and threshing
Question Statement:
A self-propelled combine harvester moves at a forward speed of $4.5\text{ km/h}$. The pickup reel of the combine has an effective diameter of $1.2\text{ m}$ and rotates at $30\text{ rpm}$. The reel index (ratio of peripheral reel speed to forward travel speed) is ________ (round off to 2 decimal places). Take $\pi = 3.1416$.
Answer Key:
1.51
Step-by-Step Solution & Explanation
1. Forward speed of the combine in $\text{m/s}$:
$v_f = 4.5 \times \frac{5}{18} = 1.25\text{ m/s}$
2. Peripheral speed of reel tips ($v_r$):
$v_r = \frac{\pi D N}{60} = \frac{3.1416 \times 1.2 \times 30}{60} = 1.885\text{ m/s}$
3. Reel Index ($\lambda$):
$\lambda = \frac{v_r}{v_f} = \frac{1.885}{1.25} = 1.508 \approx 1.51$
(Note: Standard recommended reel index for upright crops is between $1.25$ and $1.50$).