Asas Maneuvering Modeling Group (MMG)
source: MMG 3D
philosophy of theory behind MMG :
THESIS ( from p. 39 to 46)
This note will explain in brief, simple but sufficient to understand the story behind MMG and how to understand it.
Starts with:
1. Coordinate systems
2. Motion equations
3. Hydrodynamic forces - acting on hull, force by propulsion and forces by steering.
4. Tests for obtaining the coefficients:
WAKE AT PROPELLER POSITION.
1. The "level" of wake amount at the propeller position is represented by a coefficient.
2. The coefficient namely two in the MMG:
(a) wake in straight moving
(b) wake in maneuvering ( where other than straight moving).
3. The coefficient ratio of (1-wake at maneuvering coeff/ 1-wake in straight moving coeff.) is plotted against 𝜷 ( in radian). Then the plot for KVLCC2 (L-7 model) as shown below:
8. From the above eq., the value of C₂ = 1.6 at 𝜷p greater than 0. And C₂ = 1.1 at 𝜷p less than 0.
FLOW STRAIGHTENING coeff. : 𝛄R
EFFECTIVE LONGITUDINAL COORDINATE OF RUDDER POSITION in 𝜷R : ℓR
1. Both above coeff 𝛄R and ℓR are determined from below equation.
where, the key word to get 𝛄R and ℓR , again the inclination. The inclination, firstly calculated for:
(a) v'R = 𝛄R x 𝜷 . Since we know the value of v'R , then also we know 𝜷, then we can know the 𝛄R
where the inclination (v'R /𝜷) . (note: inclination also we called as derivative. It is a rate of something. Rate of increase (or decrements) of certain element versus other element. The element can be anything, including time. So, it is change of something to change of something. It is like a rate of thing to rate of thing, relatively. That's why it is called as derivatives - 2019.02.28 🙂 ). As for this case, the measure of change of v'R to the change of 𝜷.. in symbol, Δv'R / Δ𝜷. Then if we accumulate and gather in one graph, say (Δv'R / Δ𝜷)₁ , (Δv'R / Δ𝜷)₂ (Δv'R / Δ𝜷)₃ (Δv'R / Δ𝜷)₄ (Δv'R / Δ𝜷)₅ , then from there we can know the "trend" of derivatives. Then we can fitting the trend. And for this case, the fitted trend line of (Δv'R / Δ𝜷)₁₂₃₄₅ is the 𝛄R.
(b) v'R = - 𝛄R x ℓ'R x r'
where the inclination (derivatives) is : ℓ'R = Δv'R / - 𝛄R r'
the value of v'R ,
𝛄R ( is from (a) ) and
r' are known.
So, by using the same exercise as (a), then the value of ℓ'R (trend line fitting) can be found.
The question is, how to determine v'R, and before that u'R ?
Solution:
1. v'R = u'R x 𝛿FN0. In order to get it, we need to know u'R. Where u'R can be
determined(see next step).
2. u'R can be obtained from below eq. ( Eq.34 from the MMG paper).
*where, the dF'N / d𝛿 at 𝛿=𝛿FN0 can obtained from experiment. Also, 𝛿FN0.
** the value of f⍺ ( the rudder lift gradient coefficient) is determined from Fujii formulae. The Fuijii formula is
f⍺ = 6.13 𝜆 / ( 𝜆 + 2.25 )
where
𝜆 is the aspect ratio of rudder.
𝜆 = Length / area (projected) of rudder.
*Some explanation on how the f⍺ ( rudder lift gradient coefficient) works:
1. When the aspect ratio is higher, then the higher the f⍺.
2. The higher the f⍺ the larger the "effect of rudder" to the maneuvering (e.g. turning circle motion). Means, the uR in the eq. 34 above become smaller. When uR become small, means pressure is high. P=F/A. At
constant A, the F will become higher. The higher the F, the better the
maneuvering of the ship e.g turning or zig-zag. (this is so far limited to the calm water).
Discussed with Sasmito this evening ( 2019-feb-28), the fundamental of low pressure high pressure with the velocity of the fluid.
1. when the fluid velocity become high, the mass / atom/ element of air will become "loose" and so the force or energy at that respected area will be lowered.
2. So the paper, the bottom part will push the paper up because there is different pressure upper and lower part of the paper.
3. So, the paper will move upward, from high to low pressure.
discussed with Pak Cahyo - this evening on the theory behind MMG, a thesis namely : On the Determination of Hydrodynamic Coefficients for Real Time Ship Manoeuvring Simulation that was written by Nicolaas Wilhelmus Teeuwen , a DELFT UNIVERSITY product.
- conclusion from our discussion that MMG still robust and undeniably so far among the leading program / method for the simulation ship maneuvering motion in calm, and to an extend for wave condition. So far, what i have compared the in irregular waves experiment results of KVLCC2 versus the program results, the matching is almost close. But, only at low speed the closeness become low as maybe need to improve the estimation of added resistance.
- it seems that MMG's founder is highly experience/knowledgeable in understanding ship motion in calm and waves. which that makes the results so far unsung
BASIC
The very base of MMG ( or any other motion) is the Euler.
Real physics - euler
Asas dalam menggunakan euler equation, ada dua coordinate systems:
1. Global XYZ which is fixed to the ground. (also known as inertial system) link : Inertial frame
ulasan: It is useful to define a global (fixed) reference frame since quantities will only make sense if they are measured from a fixed frame. For example, we can only observe (and make sense of) the change in direction of an acceleration vector over time, if it is measured from a fixed reference frame.
2. Local XYZ frame , where is fixed to the body.
ulasan: This reference frame is attached to the rigid body and moves with it. The origin of this reference frame is located at the center of mass G of the rigid body.
(For MMG, thr location of origin is at the midship of body?)
Fundamentally-
The most general equations for the velocity and acceleration of a point in space can be expressed in terms of:
1) angular velocity,
2) angular acceleration,
3) relative velocity, and
4) relative acceleration.
detail : velocity and acceleration
Dari figure di atas, kita dengan harapannya ingin mencari velocity (laju) dan acceleration (pecutan) bagi point B di atas, yang di relatifkan dari global frame.
Ukur velocity
General untuk mengukur velocity dan kerelatifannya berdasarkan:
Di mana:
vB is the velocity of point B with respect to fixed ground (XYZ frame dlm kes ini)
vA is the velocity of point A with respect to fixed ground
w is the angular velocity of the rigid body with respect to fixed ground
r is the position vector from point A to point B
vrel is the velocity of point B relative to the moving xyz axes
Ukur acceleration
**slightly longer compared dengan velocity
di mana:
aB is the acceleration of point B with respect to fixed ground
aA is the acceleration of point A with respect to fixed ground
w is the angular velocity of the rigid body with respect to fixed ground
α is the angular acceleration of the rigid body with respect to fixed ground
r is the position vector from point A to point B
vrel is the velocity of point B relative to the moving xyz axes. Imagine if an observer were sitting on the xyz axes. The velocity vrel is what he would measure.
arel is the acceleration of point B relative to the moving xyz axes. Imagine if an observer were sitting on the xyz axes. The acceleration arelis what he would measure.
philosophy of theory behind MMG :
THESIS ( from p. 39 to 46)
This note will explain in brief, simple but sufficient to understand the story behind MMG and how to understand it.
Starts with:
1. Coordinate systems
2. Motion equations
3. Hydrodynamic forces - acting on hull, force by propulsion and forces by steering.
4. Tests for obtaining the coefficients:
- RFT - in straight moving with B = 0 ( hull drift angle equal 0).
- OTT - the ship is towed in oblique. ( B is not 0. ). This OTT is performed with r' = 0 where there is no yawing involved.
- CMT - the ship model is kept captive and towed at certain r' yawing rate. The rate is covered normally from 0.2, 0.6 and 0.8.
- RFT - in oblique towing and steady turning. This test is to obtain flow straightening coefficient test.
-----------------
In calculating hydrodynamic derivatives, LSM is applied.
substituting Eq. 7 to Eq. 28,
X
H*', YH *' and NH*' are written as a function of v0 m and r0 as
follows:
XH' = - 0.022 + (-0.040) vm'^2 +
the m' (non-dimensional mass from displacement volume of ship)
mx' and my' components from other method.
Then, plot at each force against Beta at varied yaw rate:
Then, plot at each force against Beta at varied yaw rate:
Then, next from the fitting process ( using LSM - can be seen as dotted line in the three graph above). The resistance coefficients (Ro- at the first line = 0.022) and other hydrodynamic derivatives on maneuvering as follows:
Flow straightening coefficient test
1. To find the zero normal forces at rudder, three measurement was taken. The measuring shall be considered properly so that we can do interpolation later to obtain at what rudder angle to match zero normal forces (delta_FN0).
delta_FN0 : increase with the beta and r'
2. Next, the result from the interpolation, each of them are plotted at respective beta and r' to see the trend. From the plot, we can see that the higher the hull drift angle of the ship, the larger angle of rudder degree to be set so that to maintain the zero normal force. In practice, it means the pilot need to turn the rudder more larger angle when the ship hull is drifted at larger angle ( if to maintain the straight course).
1. To find the zero normal forces at rudder, three measurement was taken. The measuring shall be considered properly so that we can do interpolation later to obtain at what rudder angle to match zero normal forces (delta_FN0).
delta_FN0 : increase with the beta and r'
2. Next, the result from the interpolation, each of them are plotted at respective beta and r' to see the trend. From the plot, we can see that the higher the hull drift angle of the ship, the larger angle of rudder degree to be set so that to maintain the zero normal force. In practice, it means the pilot need to turn the rudder more larger angle when the ship hull is drifted at larger angle ( if to maintain the straight course).
d_FN/d_delta (inclination) : seems do not increase significantly with beta and r'
3. Next, in order to know the magnitude of the " how much the rudder need to be turned with respect to the normal force" (or in other word: the ratio of rudder angle to normal force magnitude). From the next plot (d_FN/d_delta) , we can see that by increasing beta and r', it does not change the ratio of the Δnormal force: Δrudder angle. Means the magnitude of normal force to change rudder angle is consistent through out the different (increasing) angle of hull drift and r'.
3. Next, in order to know the magnitude of the " how much the rudder need to be turned with respect to the normal force" (or in other word: the ratio of rudder angle to normal force magnitude). From the next plot (d_FN/d_delta) , we can see that by increasing beta and r', it does not change the ratio of the Δnormal force: Δrudder angle. Means the magnitude of normal force to change rudder angle is consistent through out the different (increasing) angle of hull drift and r'.
WAKE AT PROPELLER POSITION.
1. The "level" of wake amount at the propeller position is represented by a coefficient.
2. The coefficient namely two in the MMG:
(a) wake in straight moving
(b) wake in maneuvering ( where other than straight moving).
3. The coefficient ratio of (1-wake at maneuvering coeff/ 1-wake in straight moving coeff.) is plotted against 𝜷 ( in radian). Then the plot for KVLCC2 (L-7 model) as shown below:
4. Firstly, the remark is on the name of the fraction.
5. It is "WAKE FRACTION" when we divide (1-wp) / (1-wp0).
6. Next, the behavior of the wake when the ship is obliquely move in minus 𝜷 and positive 𝜷. It is obvious that asymmetrical.
7. From the figure, the fitting line is plotted with the (according to the authors) equation 16 as follows:
8. From the above eq., the value of C₂ = 1.6 at 𝜷p greater than 0. And C₂ = 1.1 at 𝜷p less than 0.
FLOW STRAIGHTENING coeff. : 𝛄R
EFFECTIVE LONGITUDINAL COORDINATE OF RUDDER POSITION in 𝜷R : ℓR
1. Both above coeff 𝛄R and ℓR are determined from below equation.
where, the key word to get 𝛄R and ℓR , again the inclination. The inclination, firstly calculated for:
(a) v'R = 𝛄R x 𝜷 . Since we know the value of v'R , then also we know 𝜷, then we can know the 𝛄R
where the inclination (v'R /𝜷) . (note: inclination also we called as derivative. It is a rate of something. Rate of increase (or decrements) of certain element versus other element. The element can be anything, including time. So, it is change of something to change of something. It is like a rate of thing to rate of thing, relatively. That's why it is called as derivatives - 2019.02.28 🙂 ). As for this case, the measure of change of v'R to the change of 𝜷.. in symbol, Δv'R / Δ𝜷. Then if we accumulate and gather in one graph, say (Δv'R / Δ𝜷)₁ , (Δv'R / Δ𝜷)₂ (Δv'R / Δ𝜷)₃ (Δv'R / Δ𝜷)₄ (Δv'R / Δ𝜷)₅ , then from there we can know the "trend" of derivatives. Then we can fitting the trend. And for this case, the fitted trend line of (Δv'R / Δ𝜷)₁₂₃₄₅ is the 𝛄R.
(b) v'R = - 𝛄R x ℓ'R x r'
where the inclination (derivatives) is : ℓ'R = Δv'R / - 𝛄R r'
the value of v'R ,
𝛄R ( is from (a) ) and
r' are known.
So, by using the same exercise as (a), then the value of ℓ'R (trend line fitting) can be found.
The question is, how to determine v'R, and before that u'R ?
Solution:
1. v'R = u'R x 𝛿FN0. In order to get it, we need to know u'R. Where u'R can be
determined(see next step).
2. u'R can be obtained from below eq. ( Eq.34 from the MMG paper).
** the value of f⍺ ( the rudder lift gradient coefficient) is determined from Fujii formulae. The Fuijii formula is
f⍺ = 6.13 𝜆 / ( 𝜆 + 2.25 )
where
𝜆 is the aspect ratio of rudder.
𝜆 = Length / area (projected) of rudder.
*Some explanation on how the f⍺ ( rudder lift gradient coefficient) works:
1. When the aspect ratio is higher, then the higher the f⍺.
2. The higher the f⍺ the larger the "effect of rudder" to the maneuvering (e.g. turning circle motion). Means, the uR in the eq. 34 above become smaller. When uR become small, means pressure is high. P=F/A. At
constant A, the F will become higher. The higher the F, the better the
maneuvering of the ship e.g turning or zig-zag. (this is so far limited to the calm water).
Discussed with Sasmito this evening ( 2019-feb-28), the fundamental of low pressure high pressure with the velocity of the fluid.
1. when the fluid velocity become high, the mass / atom/ element of air will become "loose" and so the force or energy at that respected area will be lowered.
2. So the paper, the bottom part will push the paper up because there is different pressure upper and lower part of the paper.
3. So, the paper will move upward, from high to low pressure.
discussed with Pak Cahyo - this evening on the theory behind MMG, a thesis namely : On the Determination of Hydrodynamic Coefficients for Real Time Ship Manoeuvring Simulation that was written by Nicolaas Wilhelmus Teeuwen , a DELFT UNIVERSITY product.
- conclusion from our discussion that MMG still robust and undeniably so far among the leading program / method for the simulation ship maneuvering motion in calm, and to an extend for wave condition. So far, what i have compared the in irregular waves experiment results of KVLCC2 versus the program results, the matching is almost close. But, only at low speed the closeness become low as maybe need to improve the estimation of added resistance.
- it seems that MMG's founder is highly experience/knowledgeable in understanding ship motion in calm and waves. which that makes the results so far unsung
BASIC
The very base of MMG ( or any other motion) is the Euler.
Real physics - euler
Asas dalam menggunakan euler equation, ada dua coordinate systems:
1. Global XYZ which is fixed to the ground. (also known as inertial system) link : Inertial frame
ulasan: It is useful to define a global (fixed) reference frame since quantities will only make sense if they are measured from a fixed frame. For example, we can only observe (and make sense of) the change in direction of an acceleration vector over time, if it is measured from a fixed reference frame.
2. Local XYZ frame , where is fixed to the body.
ulasan: This reference frame is attached to the rigid body and moves with it. The origin of this reference frame is located at the center of mass G of the rigid body.
(For MMG, thr location of origin is at the midship of body?)
Fundamentally-
The most general equations for the velocity and acceleration of a point in space can be expressed in terms of:
1) angular velocity,
2) angular acceleration,
3) relative velocity, and
4) relative acceleration.
detail : velocity and acceleration
Dari figure di atas, kita dengan harapannya ingin mencari velocity (laju) dan acceleration (pecutan) bagi point B di atas, yang di relatifkan dari global frame.
Ukur velocity
General untuk mengukur velocity dan kerelatifannya berdasarkan:
vB is the velocity of point B with respect to fixed ground (XYZ frame dlm kes ini)
vA is the velocity of point A with respect to fixed ground
w is the angular velocity of the rigid body with respect to fixed ground
r is the position vector from point A to point B
vrel is the velocity of point B relative to the moving xyz axes
Ukur acceleration
**slightly longer compared dengan velocity
di mana:
aB is the acceleration of point B with respect to fixed ground
aA is the acceleration of point A with respect to fixed ground
w is the angular velocity of the rigid body with respect to fixed ground
α is the angular acceleration of the rigid body with respect to fixed ground
r is the position vector from point A to point B
vrel is the velocity of point B relative to the moving xyz axes. Imagine if an observer were sitting on the xyz axes. The velocity vrel is what he would measure.
arel is the acceleration of point B relative to the moving xyz axes. Imagine if an observer were sitting on the xyz axes. The acceleration arelis what he would measure.
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