ISSN (Print): 1844-6116 ISSN (Online): 1884-6116
http://www.cmu-edu.eu/jmte
Journal of Marine technology and Environment Year 2019, Vol.2 The apparent wind speed will depend on the actual wind speed Vt and the speed of the ship
= angular speed r=the radius of the rotor Coefficient C rot is introduced by the relationship
Vs which are known.
between rotor rotation speed
The calculations were made for a drift angle
very
speed
Vs `coincides with Vs . Apparent wind speed Va
small, so
U rot and apparent wind
Va . U rot CrotVa
(5)
is given by the ecuation: Speed of rotor rotation
Va Vt V 2VtVs cos 2
2 s
the apparent wind speed
(1)
Direction of the apparent wind β can be calculated from the law of the cosine at the speed triangle:
cos 1 (
Vt V V ) 2VaVs 2
2 a
U rot varies depending on
Va .
4.1 Power consumed by the rotor The resistive force and the energy of rotation (power) required to overcome this resistance created by metal rubbing is estimated by using the flat boundary theory. The Reynolds Re number, which is required for calculating the coefficient of friction C f what can be
2 s
(2)
expressed as:
Re Where
ACrotVa LRe
(6)
is the dynamic viscosity of the air and
LRe is the characteristic length, ie the circumference of
the rotor ( ,d). To find the metal friction coefficient C f , using the Reynolds number, we will use the Schlichting formula that is valid for Re values around 5 5
x 10 .
Figure 3 The Magnus Effect
cf
The Effect of Magnus is when a rotating cylinder is hit by a free air flow with a lifting force and a pulling force. The forces are strictly dependent on the rotor size, angular velocity and free flow rate. While the air mass in one part of the rotor is accelerating, the air mass on the other side is decelerated. According to the law conservation of energy, it puts a lower pressure on one side and a higher pressure on another part that creates the pushing force. This lifting force or pushing force per unit of length (L1 / l) in terms of movement este dată de legea lui Kutta-Joukowski.
L l AVA . l
0.455 1700 . (log( Re )) 2.58 Re
To calculate the total power required to rotate the rotor, the required friction force F f is given by the equation:
Ff c f A
U rot 2
2
Ar
(8)
Where: Ar = is the rotor area
(3)
Ar = dh .
Where:
= circulation; = 2r 2
(7)
The power required to rotate the rotor Pcon is:
(4)
77
(9)