A kind of test column or stake change the method for its inclination angle, sedimentation situation of change in time
Technical field
The present invention relates to a kind of method that test column or stake change its inclination angle, sedimentation situation of change in time, belong to Geotechnical Engineering applied technical field.
Background technology
In modern project, the application of post and stake is more and more extensive, but due to the impact of foundation strength, stability and various environmental factor, post or stake can be caused to occur the deformations such as skew, inclination, sedimentation, if its distortion is excessive, can have a huge impact engineering.Existing detection method, as manual detection method and embedding sensor method, method is comparatively complicated, economical not, and is not suitable for carrying out large area stake and detects in real time.
Summary of the invention
The object of the invention is, change in time for the post in modern project or stake, the test problems of its inclination angle, sedimentation change, the present invention proposes a kind of method that test column or stake change its inclination angle, sedimentation situation of change in time.
Realizing technical scheme of the present invention is, on post or stake, carries out projection mark by ruddiness cross hair device, determines inclination, the settling amount situation of change of post or stake according to its change; Ruddiness cross hair device is fixed on primary standard substance motionless by described method, makes cross laser sight post to be measured or stake, and carry out cross scale mark at post or pile body, cross scale mark overlaps with cross laser; Then using this post to be measured or stake as primary standard substance, adopt and use the same method, at its post or pile body, ruddiness cross hair device is installed, maintains static, contrast next post to be measured or stake, and mark cross scale, repeat the method; Over time, open the ruddiness cross hair device be fixed on post or pile body, if now the projection of cross laser overlaps with former scale mark, namely during this period of time there is not deformation in this post to be measured or stake; If now the projection of cross laser does not overlap with former scale mark, then this projection and former scale mark can be contrasted, read the numerical value on cross scale mark; Supposing that post or pile crown sedimentation, post or pile body inclination angle only occur for post to be measured or stake, do not consider pile crown horizontal shift, by calculating, the situation of the left and right directions inclination angle of each post to be measured or stake, fore-and-aft direction inclination angle and settling amount can be obtained; And then calculate within a period of time, the left and right directions inclination angle of single, many rows or bundle pillar or stake, fore-and-aft direction inclination angle and settling amount situation.
The present invention is a kind of method that test column or stake change its inclination angle, sedimentation situation of change in time, and step is as follows:
(1) determine primary standard substance, described primary standard substance must along with the change of time, self shift phenomenon does not occur or variable quantity is very little;
(2) ruddiness cross hair device is fixed on two diverse locations up and down of primary standard substance, the cross laser that it is irradiated can drop on surveyed post or pile body middle position, and keeping ruddiness cross hair device invariant position, the distance on upper and lower two tracking cross subpoints distance ground is respectively h and h ';
(3) at institute's test column or pile body tracking cross to the position shone, stick cross rule and paste, cross rule is overlapped with the projection of tracking cross;
(4) using detected 1# post or stake as primary standard substance, adopting uses the same method fixes ruddiness cross hair device thereon, is aimed at 2# post or stake, and in the position that tracking cross drops on, sticks cross rule and paste; Repeat this method;
(5) respectively with projection place of upper and lower cross laser for initial point sets up rectangular coordinate system, namely initial point is respectively A1 and A2; Now its coordinate is A1 (0,0), A2 (0,0);
(6) through after a period of time, open the ruddiness cross hair device being fixed on benchmark post or pile body upper and lower, cross laser is projected in the position of 1# post to be measured or pile body and cross rule and pastes position and contrast.The center that setting cross rule pastes is zero point, and on the right side of zero point and top is positive dirction, and left side and below are negative direction;
According to cross scale mark, the reading b that reading 1# post or stake top A1 point stick at horizontal rule
_{1}with the reading a that longitudinal rule sticks
_{1}; 1# post or A2 place, stake bottom, stick reading b at horizontal rule
_{1}', the reading that longitudinal rule sticks is a
_{1}'; In like manner can draw the reading situation of the posts such as 2#, 3# or stake; If now cross laser aiming point drops on the right side of pasted cross rule, so can judge this post or stake inclination to the left, if drop on the left side of cross rule, namely this post or stake are tilted to the right;
(7) because post or stake are right cylinder, cross rule pastes and pastes along pile body, and it is its axial offset that longitudinal rule pastes reading, and it is this section of arc length that horizontal rule pastes reading, therefore, and the radial deflection c of 1# post or stake top A1
_{1}as follows:
${c}_{1}=R\·sin(\frac{{b}_{1}}{2\mathrm{\π}R}\·2\mathrm{\π})$
In formula, b
_{1}for the horizontal rule of 1# post or stake top A1 point pastes reading (mm); c
_{1}for the radial deflection (mm) of 1# post or stake top A1 point; R is the radius (mm) of post (stake);
Calculate the radial offset c of 1# post (stake) bottom A2
_{1}' as follows:
${c}_{1}^{\′}=R\·sin(\frac{{b}_{1}^{\′}}{2\mathrm{\π}R}\·2\mathrm{\π})$
In formula, b
_{1}' paste reading (mm) for the horizontal rule of 1# post or stake bottom A2 point; c
_{1}' be the radial deflection (mm) of 1# post or stake bottom A2 point; R is the radius (mm) of post or stake;
In like manner, the radial offset c of n# post or stake upper point
_{n}for:
${c}_{n}=R\·sin(\frac{{b}_{n}}{2\mathrm{\π}R}\·2\mathrm{\π})$
In formula, b
_{n}for the horizontal rule of n# post or stake upper point pastes reading (mm); c
_{n}for the radial deflection (mm) of n# post or stake upper point; R is the radius (mm) of post or stake;
Calculate the radial deflection c ' of n# post or stake lower point
_{n}for:
${c}_{n}^{\′}=R\·sin(\frac{{b}_{n}^{\′}}{2\mathrm{\π}R}\·2\mathrm{\π})$
In formula, b
_{n}' paste reading (mm) for the horizontal rule of n# post or stake lower point; C '
_{n}for the radial deflection (mm) of n# post or stake lower point; R is the radius (mm) of post or stake;
(8) 1# post to be measured or stake record the axial dipole field of top A1 point is a
_{1}, radial deflection is c
_{1}, the axial dipole field of bottom A2 point is a
_{1}', radial deflection is c
_{1}'; The axial dipole field that 2# post to be measured or stake record top B1 point is a
_{2}, radial deflection is c
_{2}, the axial dipole field of bottom B2 point is a '
_{2}, radial deflection is c '
_{2}; The axial dipole field that 3# post to be measured or stake record top C1 point is a
_{3}, radial deflection is c
_{3}, the axial dipole field of bottom C2 point is a
_{3}', radial deflection is c
_{3}'; Successively, n# post to be measured or stake record the axial dipole field of upper point is a
_{n}, radial deflection is c
_{n}, the axial dipole field of lower point is a '
_{n}, radial deflection is c '
_{n};
(9) because the cross ruddiness line marking device of n# post to be measured or stake is fixed in a upper post to be measured or stake, the skew before a upper post to be measured or stake has an impact to this post to be measured or stake:
Calculate n# post or the radial actual shifts T of stake upper point
_{n} ^{on}as follows:
T
_{n} ^{on}=c
_{1}+ c
_{2}+ ... + c
_{n}
In formula, c
_{1}for the radial deflection (mm) of 1# post or stake upper point; c
_{2}for the radial deflection (mm) of 2# post or stake upper point; c
_{n}for the radial deflection (mm) of n# post or stake upper point; T
_{n} ^{on}for the radial actual shifts (mm) of n# post or stake upper point;
Calculate n# post or the radial real offset T of stake lower point
_{n} ^{under}as follows:
T
_{n} ^{under}=c
_{1}'+c
_{2}'+... + c
_{n}'
In formula, c
_{1}' be the radial deflection (mm) of 1# post or stake lower point; C '
_{2}for the radial deflection (mm) of 2# post or stake lower point; C '
_{n}for the radial deflection (mm) of n# post or stake lower point; T
_{n} ^{under}for the radial actual shifts (mm) of n# post or stake lower point;
(10) the axial actual shifts W of n# post or stake upper point is calculated
_{n} ^{on}as follows:
W
_{n} ^{on}=a
_{1}+ a
_{2}+ ... + a
_{n}
In formula, a
_{1}for the axial dipole field (mm) of 1# post or stake upper point; a
_{2}for the axial dipole field (mm) of 2# post or stake upper point; a
_{n}for the axial dipole field (mm) of n# post or stake upper point; W
_{n} ^{on}for the actual axial dipole field (mm) of n# post or stake upper point;
Calculate the axial real offset W of n# post or stake lower point
_{n} ^{under}as follows:
W
_{n} ^{under}=a
_{1}'+a '
_{2}+ ... + a '
_{n}
In formula: a
_{1}' be the axial dipole field (mm) of 1# post or stake lower point; A '
_{2}for the axial dipole field (mm) of 2# post or stake lower point; A '
_{n}for the axial dipole field (mm) of n# post or stake lower point; W
_{n} ^{under}for the axial actual shifts (mm) of n# post or stake lower point;
(11) inclination angle of post or stake is divided into the inclination angle on left and right directions and the inclination angle on fore-and-aft direction;
Calculate left and right directions inclination angle:
According to the coordinate system that step (5) is set up, the subpoint A that makes new advances
_{1}' and A
_{2}' coordinate be respectively: A
_{1}' (c
_{1}, a
_{1}); A
_{2}' (c
_{1}', a
_{1}'), connect A
_{1}', A
_{2}', by A
_{2}as initial point, set up rectangular coordinate system, by A
_{1}, A
_{1}', A
_{2}' change, so A
_{1}coordinate be (0, h
_{1}-h
_{1}'), A
_{1}' (c
_{1}, a
_{1}+ h
_{1}-h
_{1}'), A
_{2}' (c
_{1}', a
_{1}'); Calculate the left and right directions inclination angle theta of 1# stake
_{1}as follows:
${\mathrm{\θ}}_{1}=\mathrm{arctan}\frac{{c}_{1}-{c}_{1}^{\′}}{{a}_{1}+{h}_{1}-{h}_{1}^{\′}-{a}_{1}^{\′}}$
In formula: c
_{1}for the radial deflection (mm) of 1# stake upper point; c
_{1}' be the radial deflection (mm) of 1# stake lower point; a
_{1}for the axial dipole field (mm) of 1# stake upper point; a
_{1}' be the axial dipole field (mm) of 1# stake lower point; h
_{1}for the distance (mm) on 1# stake upper cross cursor subpoint and ground; h
_{1}' be the distance (mm) on 1# stake bottom tracking cross subpoint and ground;
Calculate the left and right directions inclination angle theta of n# stake
_{n}as follows:
In formula: T
_{n} ^{on}for the radial real offset (mm) of n# post or stake upper point; T
_{n} ^{under}for the radial real offset (mm) of n# post or stake lower point; W
_{n} ^{on}for the axial real offset (mm) of n# post or stake upper point; W
_{n} ^{under}for the axial real offset (mm) of n# post or stake lower point; h
_{n}for the distance (mm) on n# stake upper cross cursor subpoint and ground; H '
_{n}for the distance (mm) on n# stake bottom tracking cross subpoint and ground;
(12) 1# post or stake sedimentation value is calculated:
L
_{1}subpoint A during for irradiating first
_{1}a
_{2}line, L
_{2}for again detecting subpoint A during irradiation
_{1}' A
_{2}' line, L
_{3}for the subpoint A that identical inclination angle does not produce sedimentation only occurs around termination for hypothesis post or stake
_{1}" A
_{2}" line, S
_{1}be post or stake sedimentation value;
By geometric relationship, then there is A
_{1}a
_{2}//A
_{1}" A
_{2}", EF//A
_{2}a
_{2}", A
_{2}a
_{2}" //DG, A
_{2}" D//A
_{2}c,
So, S
_{1}=S
_{2}=S
_{3}; S again
_{3}=m
_{1}+ m
_{2}, therefore post or stake sedimentation value S
_{1}=m
_{1}+ m
_{2};
Calculate m
_{1}:
At Δ DGA
_{2}" in, due to EA
_{2}'=EA
_{2}", so
therefore:
Due to
$\frac{{\mathrm{EA}}_{2}^{\′}}{sin\∠{\mathrm{EA}}_{2}^{\′\′}{A}_{2}^{\′}}=\frac{{A}_{2}^{\′}{A}_{2}^{\′\′}}{{\mathrm{sin\θ}}_{1}},$ Wherein EA
_{2}'=h
_{1}',
Draw:
At Δ DA
_{2}' A
_{2}" in, due to
$\frac{{A}_{2}^{\′}{A}_{2}^{\′\′}}{\mathrm{sin}\∠{A}_{2}^{\′\′}{\mathrm{DA}}_{2}^{\′}}=\frac{{m}_{1}}{\mathrm{sin}\∠{\mathrm{DA}}_{2}^{\′\′}{A}_{2}^{\′}}$
Calculate m
_{2}:
At Δ A
_{2}in ' CG, ∠ CA
_{2}' G=θ
_{1}, CA
_{2}'=c
_{1}, so
Therefore, sedimentation value is:
So, the sedimentation value of n# post or stake is:
(13) inclination angle on fore-and-aft direction is calculated:
L
_{1}subpoint A during for irradiating first
_{1}a
_{2}line, L
_{2}for again detecting subpoint A during irradiation
_{1}' A
_{2}' line, L
_{3}for the subpoint A of sedimentation does not occur hypothesis
_{1}" A
_{2}", S
_{1}for 1# treats the sedimentation value of peg;
${\mathrm{\φ}}_{n}=acrcos\left(\frac{{S}_{1}+{h}_{1}^{\′}}{{h}_{1}^{\′}+{a}_{1}^{\′}}\right)$
In formula: a
_{1}' be the axial offset (mm) of 1# post or stake lower point; h
_{1}' for 1# post or projection place of stake tracking cross distance ground height (mm); φ
_{1}for the inclination angle (°) on the fore-and-aft direction of 1# post or stake;
Inclination angle on the fore-and-aft direction of n# post or stake is:
(14) n# post or stake left and right directions inclination angle theta
_{n}as follows:
The sedimentation value S of n# post or stake
_{n}for:
Declination angle on the fore-and-aft direction of n# post or stake
_{n}for:
In formula: T
_{n} ^{on}for the radial real offset (mm) of n# post or stake upper point; T
_{n} ^{under}for the radial real offset (mm) of n# post or stake lower point; W
_{n} ^{on}for the axial real offset (mm) of n# post or stake upper point; W
_{n} ^{under}for the axial real offset (mm) of n# post or stake lower point; h
_{n}for the distance (mm) on n# post or stake upper cross cursor subpoint and ground; H '
_{n}for the distance (mm) on n# post or stake bottom tracking cross subpoint and ground.
The invention has the beneficial effects as follows, the present invention is by the application be projected on post (stake) to ruddiness cross hair device and cross laser, can measuring column (stake) along with the change of time, the situation of its left and right directions inclination angle, fore-and-aft direction inclination angle and sedimentation change.The inventive method is simple, practical; For the detection of the inclination angle of engineering center pillar or stake and sedimentation situation over time provides one approach simply and easily.
The present invention is applicable to test column or stake changes in time, the situation that its left and right directions inclination angle, fore-and-aft direction inclination angle and settling amount change.
Accompanying drawing explanation
Fig. 1 is that ruddiness cross hair device is fixed and projected position schematic diagram;
Fig. 2 is that cross rule overlaps with the projection of tracking cross schematic diagram;
Fig. 3 fixes and perspective view for next post to be measured or stake ruddiness cross hair device;
In figure, 1 is benchmark post or stake; 2 is 1# test column or stake; 3 is 2# test column or stake; 4 is 3# test column or stake; 5 is 4# test column or stake; L is the distance between benchmark post (stake) and test column (stake);
Fig. 4 is for initial point sets up rectangular coordinate system schematic diagram with projection place of upper and lower cross laser;
Fig. 5 is that cross rule pastes positive and negative regulation schematic diagram;
Fig. 6 is the right side schematic view that cross laser aiming point drops on cross rule;
Fig. 7 is post to be measured or stake radial offset schematic diagram, the vertical view of A1 point;
Fig. 8 is upper and lower subpoint coordinate schematic diagram;
Fig. 9 is the left and right directions inclination angle schematic diagram calculating 1# post or stake;
Figure 10 is for calculating 1# post or stake sedimentation value schematic diagram;
Figure 11 is for calculating 1# post or stake fore-and-aft direction inclination angle schematic diagram;
Embodiment
The present invention is a kind of method that test column or stake change its inclination angle, sedimentation situation of change in time, and concrete enforcement is carried out according to the following steps:
Step 1:
First determine primary standard substance, can by making or selecting to determine primary standard substance, this primary standard substance must along with the change of time, self there is not the phenomenons such as skew or variable quantity very little.
Step 2:
Ruddiness cross hair device is fixed on two diverse locations up and down of primary standard substance, the cross laser that it is irradiated can drop on surveyed post or pile body middle position, and keeping ruddiness cross hair device invariant position, the distance on upper and lower two tracking cross subpoints distance ground is respectively h and h '; As shown in Figure 1.
Step 3:
At institute's test column or pile body tracking cross to the position shone, stick cross rule and paste, cross rule is overlapped with the projection of tracking cross.As shown in Figure 2.
Step 4:
Using detected 1# post or stake as primary standard substance, adopting uses the same method fixes ruddiness cross hair device thereon, is aimed at 2# post or stake, and in the position that tracking cross drops on, sticks cross rule and paste.Repeat this method.As shown in Figure 3.
Step 5:
Respectively with projection place of upper and lower cross laser for initial point sets up rectangular coordinate system, namely initial point is respectively A1 and A2.Now its coordinate is A1 (0,0), A2 (0,0); As shown in Figure 4.
Step 6:
Through after a period of time, open the ruddiness cross hair device being fixed on benchmark post or pile body upper and lower, cross laser is projected in the position of 1# post to be measured or pile body and cross rule and pastes position and contrast.The center that setting cross rule pastes is zero point, and on the right side of zero point and top is positive dirction, and left side and below are negative direction.As shown in Figure 5.
According to cross scale mark, the reading b that reading 1# post or stake top A1 stick at horizontal rule
_{1}with the reading a that longitudinal rule sticks
_{1}.1# post or A2 place, stake bottom, stick reading b at horizontal rule
_{1}', the reading that longitudinal rule sticks is a
_{1}'.In like manner can draw the reading situation of the posts such as 2#, 3# or stake.As Fig. 6: if now cross laser aiming point drop on the right side of cross rule of pasting, so can judge stake inclination to the left, if drop on the left side of cross rule, namely stake is tilted to the right.
Step 7:
Because post or stake are right cylinder, cross rule pastes and pastes along pile body, and it is its axial offset that longitudinal rule pastes reading, and it is this section of arc length that horizontal rule pastes reading, as shown in Figure 7, therefore, and the radial deflection c of 1# stake top A1
_{1}as follows:
${c}_{1}=R\·sin(\frac{{b}_{1}}{2\mathrm{\π}R}\·2\mathrm{\π})$
In formula, b
_{1}for the horizontal rule of 1# post or stake top A1 point pastes reading (mm); c
_{1}for the radial deflection (mm) of 1# post or stake top A1 point; R is the radius (mm) of post or stake.
Calculate the radial offset c of 1# post or stake bottom A2
_{1}' as follows:
${c}_{1}^{\′}=R\·sin(\frac{{b}_{1}^{\′}}{2\mathrm{\π}R}\·2\mathrm{\π})$
In formula, b
_{1}' paste reading (mm) for the horizontal rule of 1# post or stake bottom A2 point; c
_{1}' be the radial deflection (mm) of 1# post or stake bottom A2 point; R is the radius (mm) of post or stake.
In like manner, the radial offset c of n# post or stake upper point
_{n}for:
${c}_{n}=R\·sin(\frac{{b}_{n}}{2\mathrm{\π}R}\·2\mathrm{\π})$
In formula, b
_{n}for the horizontal rule of n# post or stake upper point pastes reading (mm); c
_{n}for the radial deflection (mm) of n# post or stake upper point; R is the radius (mm) of post or stake.
Calculate the radial deflection c ' of n# post or stake lower point
_{n}for:
${c}_{n}^{\′}=R\·sin(\frac{{b}_{n}^{\′}}{2\mathrm{\π}R}\·2\mathrm{\π})$
In formula, b
_{n}' paste reading (mm) for the horizontal rule of n# post or stake lower point; C '
_{n}for the radial deflection (mm) of n# post or stake lower point; R is the radius (mm) of post or stake.
Step 8:
The axial dipole field that 1# post to be measured or stake record top A1 point is a
_{1}, radial deflection is c
_{1}, the axial dipole field of bottom A2 point is a
_{1}', radial deflection is c
_{1}'; The axial dipole field that 2# post to be measured or stake record top B1 point is a
_{2}, radial deflection is c
_{2}, the axial dipole field of bottom B2 point is a '
_{2}, radial deflection is c '
_{2}; The axial dipole field that 3# post to be measured or stake record top C1 point is a
_{3}, radial deflection is c
_{3}, the axial dipole field of bottom C2 point is a
_{3}', radial deflection is c
_{3}'; Successively, n# post to be measured or stake record the axial dipole field of upper point is a
_{n}, radial deflection is c
_{n}, the axial dipole field of lower point is a '
_{n}, radial deflection is c '
_{n}.
Step 9:
Because the cross ruddiness line marking device of n# post to be measured or stake is fixed in a upper post to be measured or stake, the skew before a upper post to be measured or stake is on the impact of this post to be measured (stake).
Calculate n# post or the radial actual shifts T in stake top
_{n} ^{on}as follows:
T
_{n} ^{on}=c
_{1}+ c
_{2}+ ... + c
_{n}
In formula, c
_{1}for the radial deflection (mm) of 1# post or stake upper point; c
_{2}for the radial deflection (mm) of 2# post or stake upper point; c
_{n}for the radial deflection (mm) of n# post or stake upper point; T
_{n} ^{on}for the radial actual shifts (mm) of n# post or stake upper point.
Calculate n# post or the radial real offset T of stake lower point
_{n} ^{under}as follows:
T
_{n} ^{under}=c
_{1}'+c
_{2}'+... + c
_{n}'
In formula, c
_{1}' be the radial deflection (mm) of 1# post or stake lower point; C '
_{2}for the radial deflection (mm) of 2# post or stake lower point; C '
_{n}for the radial deflection (mm) of n# post or stake lower point; T
_{n} ^{under}for the radial actual shifts (mm) of n# post or stake lower point.
Step 10:
Calculate the axial actual shifts W on n# post or stake top
_{n} ^{on}as follows:
W
_{n} ^{on}=a
_{1}+ a
_{2}+ ... + a
_{n}
In formula, a
_{1}for the axial dipole field (mm) of 1# post or stake upper point; a
_{2}for the axial dipole field (mm) of 2# post or stake upper point; a
_{n}for the axial dipole field (mm) of n# post or stake upper point; W
_{n} ^{on}for the actual axial dipole field (mm) of n# post or stake upper point.
Calculate the axial real offset W of n# post or stake lower point
_{n} ^{under}as follows:
W
_{n} ^{under}=a
_{1}'+a '
_{2}+ ... + a '
_{n}
In formula: a
_{1}' be the axial dipole field (mm) of 1# post or stake lower point; A '
_{2}for the axial dipole field (mm) of 2# post or stake lower point; A '
_{n}for the axial dipole field (mm) of n# post or stake lower point; W
_{n} ^{under}for the axial actual shifts (mm) of n# post or stake lower point.
Step 11:
The inclination angle of post or stake is divided into the inclination angle on left and right directions and the inclination angle on fore-and-aft direction.
Calculate left and right directions inclination angle.According to step 5 set up coordinate system, the subpoint A that makes new advances
_{1}' and A
_{2}' coordinate be respectively: A
_{1}' (c
_{1}, a
_{1}); A
_{2}' (c
_{1}', a
_{1}'), connect A
_{1}', A
_{2}', be illustrated in fig. 8 shown below.
By A
_{2}as initial point, set up rectangular coordinate system, by A
_{1}, A
_{1}', A
_{2}' change, so A
_{1}coordinate be (0, h
_{1}-h
_{1}'), A
_{1}' (c
_{1}, a
_{1}+ h
_{1}-h
_{1}'), A
_{2}' (c
_{1}', a
_{1}'); As shown in Figure 9.
Calculate the left and right directions inclination angle theta of 1# post or stake
_{1}as follows:
${\mathrm{\θ}}_{1}=\mathrm{arctan}\frac{{c}_{1}-{c}_{1}^{\′}}{{a}_{1}+{h}_{1}-{h}_{1}^{\′}-{a}_{1}^{\′}}$
In formula: c
_{1}for the radial deflection (mm) of 1# post or stake upper point; c
_{1}' be the radial deflection (mm) of 1# post or stake lower point; a
_{1}for the axial dipole field (mm) of 1# post or stake upper point; a
_{1}' be the axial dipole field (mm) of 1# post or stake lower point; h
_{1}for the distance (mm) on 1# post or stake upper cross cursor subpoint and ground; h
_{1}' be the distance (mm) on 1# post or stake bottom tracking cross subpoint and ground.
Calculate the left and right directions inclination angle theta of n# post or stake
_{n}as follows:
In formula: T
_{n} ^{on}for the radial real offset (mm) of n# post or stake upper point; T
_{n} ^{under}for the radial real offset (mm) of n# post or stake lower point; W
_{n} ^{on}for the axial real offset (mm) of n# post or stake upper point; W
_{n} ^{under}for the axial real offset (mm) of n# post or stake lower point; h
_{n}for the distance (mm) on n# post or stake upper point tracking cross subpoint and ground; H '
_{n}for the distance (mm) on n# post or stake lower point tracking cross subpoint and ground.
Step 12:
Calculate 1# post or stake sedimentation value:
As shown in Figure 10, L
_{1}subpoint A during for irradiating first
_{1}a
_{2}line, L
_{2}for again detecting subpoint A during irradiation
_{1}' A
_{2}' line, L
_{3}for the subpoint A that identical inclination angle does not produce sedimentation only occurs around termination for hypothesis post or stake
_{1}" A
_{2}" line, S in figure
_{1}be post or stake sedimentation value.By geometric relationship, then there is A
_{1}a
_{2}//A
_{1}" A
_{2}", EF//A
_{2}a
_{2}", A
_{2}a
_{2}" //DG, A
_{2}" D//A
_{2}c, so, S
_{1}=S
_{2}=S
_{3}.S again
_{3}=m
_{1}+ m
_{2}, therefore post or stake sedimentation value S
_{1}=m
_{1}+ m
_{2}.
(1) m is calculated
_{1}.
At Δ DGA
_{2}" in, due to EA
_{2}'=EA
_{2}", so
therefore:
Due to
$\frac{{\mathrm{EA}}_{2}^{\′}}{sin\∠{\mathrm{EA}}_{2}^{\′\′}{A}_{2}^{\′}}=\frac{{A}_{2}^{\′}{A}_{2}^{\′\′}}{{\mathrm{sin\θ}}_{1}},$ Wherein EA
_{2}'=h
_{1}',
Draw:
At Δ DA
_{2}' A
_{2}" in, due to
$\frac{{A}_{2}^{\′}{A}_{2}^{\′\′}}{\mathrm{sin}\∠{A}_{2}^{\′\′}{\mathrm{DA}}_{2}^{\′}}=\frac{{m}_{1}}{\mathrm{sin}\∠{\mathrm{DA}}_{2}^{\′\′}{A}_{2}^{\′}}$
(2) m is calculated
_{2}.
At Δ A
_{2}in ' CG, ∠ CA
_{2}' G=θ
_{1}, CA
_{2}'=c
_{1},
So,
${m}_{2}=\frac{{A}_{2}^{\′}C}{{\mathrm{cos\θ}}_{1}}=\frac{{c}_{1}}{{\mathrm{cos\θ}}_{1}}$
Therefore, 1# post or stake sedimentation value are:
So, the sedimentation value of n# post or stake is:
Step 13:
Calculate the inclination angle on fore-and-aft direction:
As shown in figure 11, L
_{1}subpoint A during for irradiating first
_{1}a
_{2}line, L
_{2}for again detecting subpoint A during irradiation
_{1}' A
_{2}' line, L
_{3}for the subpoint A of sedimentation does not occur hypothesis
_{1}" A
_{2}", S
_{1}for 1# treats the sedimentation value of peg.
${\mathrm{\φ}}_{n}=acrcos\left(\frac{{S}_{1}+{h}_{1}^{\′}}{{h}_{1}^{\′}+{a}_{1}^{\′}}\right)$
In formula: a
_{1}' be the axial offset (mm) of 1# post or stake lower point; h
_{1}' for 1# post or projection place of stake tracking cross distance ground height (mm); φ
_{1}for the inclination angle (°) on the fore-and-aft direction of 1# post or stake.
Inclination angle on the fore-and-aft direction of n# post or stake is:
Step 14:
The left and right directions inclination angle theta of n# post or stake
_{n}as follows:
The sedimentation value S of n# post or stake
_{n}for:
Declination angle on the fore-and-aft direction of n# post or stake
_{n}for:
In formula: T
_{n} ^{on}for the radial real offset (mm) of n# post or stake upper point; T
_{n} ^{under}for the radial real offset (mm) of n# post or stake lower point; W
_{n} ^{on}for the axial real offset (mm) of n# post or stake upper point; W
_{n} ^{under}for the axial real offset (mm) of n# post or stake lower point; h
_{n}for the distance (mm) on n# post or stake upper cross cursor subpoint and ground; H '
_{n}for the distance (mm) on n# post (stake) bottom tracking cross subpoint and ground.