Agriculture Reference
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a
b
1000
800
a
600
b
400
200
0
0
2
4 6
Displacement, mm
8
10
12
Fig. 5.3
(
a
) Total (
E
t
), cutting (
E
c
), and stalk (
E
s
) energy required for impact cut of sugar cane
stalks of different diameters. Adapted from [
20
]. (
b
)CuttingforcerequiredtocutaMiscanthus
stem across its diameter. a, flat cutting blade; b, serrated cutting blade. Adapted from [
9
]
uniform stubble height. By equating cutting forces with the expected rigidity of the
plant, Persson and ASAE [
15
] provides an equation for this critical speed
æ
ö
z
r
d
FF
m
-
cg
v
=
x
b
ç
1
+
÷
(5.1)
k
s
2
è
ø
p
g
where
v
k
= critical knife velocity, m s
−1
,
d
s
= stalk diameter, mm,
F
x
= cutting force,
N,
F
b
= bending resistance of stump, N,
m
p
= mass of cut portion of plant, kg,
z
cg
= height
of center of gravity of cut plant, m,
r
g
= radius of gyration of cut portion of plant, m.
A simple approximation to this equation can be obtained by assuming that
r
g
=
z
cg
[
16
].Criticalcuttingspeedsingrassaretypicallyabout25 ms
−1
, but commercial
impactcuttingmachineryoperatesat60ms
−1
or higher cutting speeds.
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