Tianhemast analyse des forces de vent

Wind Resistance – Mast Wind Resistance and Calculation Method

1) Knowledge of Mast Wind Resistance
Mast wind resistance is one of the important technical indicators of mast products. Every customer wants to know how much wind force that their mast can withstand after installing loads; however, hardly anyone can answer this question accurately.This is because mast’s wind resistance performance is determined by the following three factors:
A Mast structure and material
B Use height of mast
C Weight, volume and shape of loads
In case that the above three conditions are provided, we can use the following three methods to calculate specific wind resistance index:
（1） Theoretical calculation: Use finite element analysis and other methods.
（2）Simulation experiment: Convert different scales of wind power into wind pressure, and then use physical method (tensiometer) for testing.
（3） Wind tunnel experiment: Place the mast and loads in the wind tunnel, and simulate wind speed for testing.
In the above three methods, the third method can provide a more realistic value. However, the cost and condition requirements for wind tunnel experiment are very high. For example, is there a big enough wind tunnel for experiment of an 18-meter-high mast with loads? Is the experiment possible ? How much will it cost? These are all problems. Therefore, for mast manufacturers, wind resistance index of mast can only be provided using the first two methods

2）Calculation Method of Mast Wind Resistance
(This calculation method is a theoretical calculation formula for unloaded mast provided by experts invited by our company according to material, structure and height of our masts, and for reference only.)
For example: The wind resistance performance of A4-270-2300-7600 lifting rod is calculated according to benchmark wind speed of 100km/h.
1、Technical Conditions

　　1.1、Designed benchmark wind speed of lifting rod ▽=100km/h≈28m/s
1.2、When ▽= 28m/s, estimate wind resistance D borne by the lifting rod.
1.3、The lifting rod has a total of 4 segments. Specific size is shown in the table.

Tube	Outer diameter	284	242	229	202
Tube	Length	1700	1700	1700	1700

Wind scale and Wind speed，Wind force list (for designed)
Wind scale	Wind name	wind speed		W0=V2/16（kg/m²)，10N/m²	Signs of land surface objects	Sea state
Wind scale	Wind name	km/h	（m/s）	W0=V2/16（kg/m²)，10N/m²	Signs of land surface objects	Sea state
8	Fresh gale	62-74	17.2-20.7	18.49-26.78	Branchlets broken; it is very difficult for people to move ahead	Wild wave
9	Strong gale	75-88	20.8-24.4	27.04-37.21	Buildings are slightly damaged	Very high sea
10	Whole gale	89-102	24.5-28.4	37.52-50.41	Can uproot trees and damage buildings	Very high sea
11	Storm	103-117	28.5-32.6	50.77-66.42	Rarely seen on land; there must be extensive destruction if it is on land	Very high sea
12	Hurricane	>117	32.7-36.9	66.42-85.1	Very rarely seen on land; great destructive power	Monstrous wave

2.Wind Resistance Calculation
2.1 Bending Resistant Section Coefficient
As the bottom of topmost tube is the weakest part of mast and bears large bending moment, tubes with outer diameter of 202mm can ensure normal use and guarantee the use of the entire mast.
Coefficient of Bending Resistant Section of Tubes with 202mm Outer Diameter

w=πd²／32 ﹛1-﹙d_o/d ﹚⁴﹜=3.14×202²/32 ﹛1－﹙190/202 ﹚⁴﹜=181332mm²

2.2 Gust wind coefficient

The so-called gust Kg is the ratio of maximum instantaneous wind speed V2 and mean wind speed V2 within observation time. It is related to observation time, average wind speed, topography, surface roughness, recurrence interval of benchmark wind speed, and other factors. Generally, Kg is between 1.2 and 1.5, here Kg=1.3.
V₂=▽K_g=28×1.3=36.4m/s

2.3 Reynolds Number of Lifting Rod in Different Diameter Segments
2.3.1Reynolds Number
R₂=V₂d/V= 36.4×0.202/0.15×10^﹣4=4.9×10³
V－Air Kinematic Viscosity，0.15×10^﹣4m²／s

d－Tube Diameter
2.3.2
Resistance coefficient CD of the lifting rod is determined according to the change range of Reynolds number of various segments of the lifting rod.
As the lifting rod is relatively long and has smooth surface, we can regard it as a smooth two-dimensional rod. The figure below shows the relation curve between resistance coefficient CD of the smooth two-dimensional cylinder and Reynolds number Re.

It can be seen from the curve that the Re range of the lifting rod is just within the area of CD=1.2.
2.4 Wind Resistance of Lifting Rod at the Top of Topmost Segment
D=C_D·2/2PV₂²dlK_g²

=1.2×２/20×36.4²×0.202×1.7×1.3²

=57.67kg

2.5 Strength Check
σ_max=M_max/W=37.4×20×27×2000／20222=5.4Mpa

6063-T6下σ=205Mpa，To ensure safety, takeσ=160Mpa
As σmax<σ, the mast can withstand 100km/h of wind speed. In case of mechanical self-locking structure, the wind power borne by the mast can be multiplied to 11 scale wind
3）Methods to Improve Wind Resistance Performance of Mast
If the mast with existing specifications is used, the following several methods can be adopted to improve mast’s wind resistance:
1） Lift and lower the mast according to weather conditions. Lower the mast in case of high wind; lift the mast in case of low-speed wind.
2）Use wind-resistant cordelle. Use cordelle correct and timely, in order to greatly increase the mast’s wind resistance. How to use cordelle is shown in the figure below.

Set loads’ windward area of 0.85m2, and install guylines at the top most segment of the mast. The corresponding wind resistance strength of different cordelle angles is shown in the table.