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18 - AgriPV - Coffee Plantation with Tree Modeling.py
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18 - AgriPV - Coffee Plantation with Tree Modeling.py
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#!/usr/bin/env python
# coding: utf-8
# In[ ]:
# This information helps with debugging and getting support :)
import sys, platform
import pandas as pd
import bifacial_radiance as br
print("Working on a ", platform.system(), platform.release())
print("Python version ", sys.version)
print("Pandas version ", pd.__version__)
print("bifacial_radiance version ", br.__version__)
# # 18 - AgriPV - Coffee Plantation with Tree Modeling
# ## Designing for adecuate crop shading
# This journal supports the process of designing a solar panel configuration to appropriately represent ideal shading conditions for coffee production underneath elevated solar panels.
#
# The coffee trees would be under and/or in between elevated solar panels (panels would be elevated 6, 8, or 10 ft tall). The light/shade analysis helps determine appropriate panel heights and spacings t0 achieve appropriate shading. The desired level of shading is maximum of 30% (i.e., 70% of normal, unshaded light).
#
# Details:
# * The coffee plants are expected to be \~5 ft tall. (5-6 ft tall and 3 ft wide (<a href="https://realgoodcoffeeco.com/blogs/realgoodblog/how-to-grow-a-coffee-plant-at-home#:~:text=However%2C%20you%20must%20keep%20in,tall%20and%203%20feet%20wide">Reference</a>)
# * Location: 18.202142, -66.759187; (18°12'07.7"N 66°45'33.1"W)
# * Desired area of initial analysis: 400-600 ft2 (37-55 m2)
# * Racking: Fixed-tilt panels
# * Panel size: 3.3 feet x 5.4 feet (1m x 1.64m)
# * Analysis variations:
# * a. Panel height: would like to examine heights of 6 ft, 8 ft, and 10 ft hub height.
# * b. Panel spacing (N/W): would like to look at multiple distances (e.g., 2 ft, 3 ft, 4 ft)
# * c. Inter-Row spacing (E/W): would like to look at multiple distances (e.g., 2 ft, 3 ft, 4 ft)!
#
#
# Steps on this Journal:
# 1. <a href='#step1'>Loop to Raytrace and sample irradiance at where Three would be located </a>
# 2. <a href='#step2'> Calculate GHI for Comparisons </a>
# * <a href='#step2a'> Option 1: Raytrace of Empty Field</a>
# * <a href='#step2b'> Option 2: Weather File</a>
# 3. <a href='#step3'> Compile Results</a>
# 4. <a href='#step4'> Plot Results</a>
# 5. <a href='#step5'> Raytrace with Tree Geometry</a>
# 1. <a href='#step5a'>Tree Parameters</a>
# 2. <a href='#step5b'>Loop to Raytrace and Sample Irradiance at Each side of the Tree (N, S, E, W)</a>
# 3. <a href='#step5c'>Single simulation until MakeOct for Getting a PRETTY IMAGE</a>
# 6. <a href='#step6'> Compile Results</a>
# 7. <a href='#step7'> Plot</a>
#
#
#
# 
#
#
# While we have HPC scripts to do the below simulation, this journals runs all of the above so it might take some time, as there are 109 combinations of parameters explored
# In[ ]:
import bifacial_radiance
import os
from pathlib import Path
import numpy as np
import pandas as pd
# In[ ]:
testfolder = str(Path().resolve().parent.parent / 'bifacial_radiance' / 'TEMP' / 'Tutorial_18')
if not os.path.exists(testfolder):
os.makedirs(testfolder)
resultsfolder = os.path.join(testfolder, 'results')
# ## General Parameters and Variables
# In[ ]:
lat = 18.202142
lon = -66.759187
albedo = 0.25 # Grass value from Torres Molina, "Measuring UHI in Puerto Rico" 18th LACCEI
# International Multi-Conference for Engineering, Education, and Technology
ft2m = 0.3048
# Loops
clearance_heights = np.array([6.0, 8.0, 10.0])* ft2m
xgaps = np.array([2, 3, 4]) * ft2m
Ds = np.array([2, 3, 4]) * ft2m # D is a variable that represents the spacing between rows, not-considering the collector areas.
tilts = [round(lat), 10]
x = 1.64
y = 1
azimuth = 180
nMods = 20
nRows = 7
numpanels = 1
module_name = 'test-module'
hpc = False
sim_general_name = 'tutorial_18'
# In[ ]:
if not os.path.exists(os.path.join(testfolder, 'EPWs')):
demo = bifacial_radiance.RadianceObj('test',testfolder)
epwfile = demo.getEPW(lat,lon)
else:
epwfile = r'EPWs\PRI_Mercedita.AP.785203_TMY3.epw'
# <a id='step1'></a>
# ## 1. Loop to Raytrace and sample irradiance at where Three would be located
# In[ ]:
demo = bifacial_radiance.RadianceObj(sim_general_name,str(testfolder))
demo.setGround(albedo)
metdata = demo.readWeatherFile(epwfile)
demo.genCumSky()
# In[ ]:
for ch in range (0, len(clearance_heights)):
clearance_height = clearance_heights[ch]
for xx in range (0, len(xgaps)):
xgap = xgaps[xx]
for tt in range (0, len(tilts)):
tilt = tilts[tt]
for dd in range (0, len(Ds)):
pitch = y * np.cos(np.radians(tilt))+Ds[dd]
sim_name = (sim_general_name+'_ch_'+str(round(clearance_height,1))+
'_xgap_'+str(round(xgap,1))+\
'_tilt_'+str(round(tilt,1))+
'_pitch_'+str(round(pitch,1)))
# Coffe plant location at:
coffeeplant_x = (x+xgap)/2
coffeeplant_y = pitch/2
demo.makeModule(name=module_name, x=x, y=y, xgap = xgap)
sceneDict = {'tilt':tilt, 'pitch':pitch, 'clearance_height':clearance_height, 'azimuth':azimuth,
'nMods': nMods, 'nRows':nRows}
scene = demo.makeScene(module=module_name, sceneDict=sceneDict, radname=sim_name)
octfile = demo.makeOct(octname = demo.basename )
analysis = bifacial_radiance.AnalysisObj(octfile=octfile, name=sim_name)
# Modify sensor position to coffee plant location
frontscan, backscan = analysis.moduleAnalysis(scene=scene, sensorsy=1)
groundscan = frontscan.copy()
groundscan['xstart'] = coffeeplant_x
groundscan['ystart'] = coffeeplant_y
groundscan['zstart'] = 0.05
groundscan['orient'] = '0 0 -1'
analysis.analysis(octfile, name=sim_name+'_Front&Back', frontscan=frontscan, backscan=backscan)
analysis.analysis(octfile, name=sim_name+'_Ground&Back', frontscan=groundscan, backscan=backscan)
# <a id='step2'></a>
# ## 2. Calculate GHI for Comparisons
# <a id='step2a'></a>
#
# ### Option 1: Raytrace of Empty Field
# In[ ]:
sim_name = 'EMPTY'
demo.makeModule(name=module_name, x=0.001, y=0.001, xgap = 0)
sceneDict = {'tilt':0,'pitch':2,'clearance_height':0.005,'azimuth':180, 'nMods': 1, 'nRows': 1}
scene = demo.makeScene(module=module_name,sceneDict=sceneDict, radname = sim_name)
octfile = demo.makeOct(octname = demo.basename)
analysis = bifacial_radiance.AnalysisObj(octfile=octfile, name=sim_name)
frontscan, backscan = analysis.moduleAnalysis(scene=scene, sensorsy=1)
emptyscan = frontscan.copy()
emptyscan['xstart'] = 3
emptyscan['ystart'] = 3
emptyscan['zstart'] = 0.05
emptyscan['orient'] = '0 0 -1'
emptybackscan = emptyscan.copy()
emptybackscan['orient'] = '0 0 1'
analysis.analysis(octfile, name='_EMPTYSCAN', frontscan=emptyscan, backscan=emptybackscan)
resname = os.path.join(resultsfolder, 'irr__EMPTYSCAN.csv')
data = pd.read_csv(resname)
puerto_rico_Year = data['Wm2Front'][0]
print("YEARLY TOTAL Wh/m2:", puerto_rico_Year)
# <a id='step2b'></a>
# ### Option 2: Weather File
# In[ ]:
# Indexes for start of each month of interest in TMY3 8760 hours file
#starts = [2881, 3626, 4346, 5090, 5835]
#ends = [3621, 4341, 5085, 5829, 6550]
starts = [metdata.datetime.index(pd.to_datetime('2021-05-01 6:0:0 -7')),
metdata.datetime.index(pd.to_datetime('2021-06-01 6:0:0 -7')),
metdata.datetime.index(pd.to_datetime('2021-07-01 6:0:0 -7')),
metdata.datetime.index(pd.to_datetime('2021-08-01 6:0:0 -7')),
metdata.datetime.index(pd.to_datetime('2021-09-01 6:0:0 -7'))]
ends = [metdata.datetime.index(pd.to_datetime('2021-05-31 18:0:0 -7')),
metdata.datetime.index(pd.to_datetime('2021-06-30 18:0:0 -7')),
metdata.datetime.index(pd.to_datetime('2021-07-31 18:0:0 -7')),
metdata.datetime.index(pd.to_datetime('2021-08-31 18:0:0 -7')),
metdata.datetime.index(pd.to_datetime('2021-09-30 18:0:0 -7'))]
ghi_PR=[]
for ii in range(0, len(starts)):
start = starts[ii]
end = ends[ii]
ghi_PR.append(demo.metdata.ghi[start:end].sum())
puerto_Rico_Monthly = ghi_PR # Wh/m2
puerto_Rico_YEAR = demo.metdata.ghi.sum() # Wh/m2
print("Monthly Values May-Sept:", puerto_Rico_Monthly, "Wh/m2")
print("Year Values", puerto_Rico_YEAR, "Wh/m2")
# <a id='step3'></a>
# ## 3. Compile Results
# In[ ]:
ch_all = []
xgap_all = []
tilt_all = []
pitch_all = []
FrontIrrad = []
RearIrrad = []
GroundIrrad = []
for ch in range (0, len(clearance_heights)):
clearance_height = clearance_heights[ch]
for xx in range (0, len(xgaps)):
xgap = xgaps[xx]
for tt in range (0, len(tilts)):
tilt = tilts[tt]
for dd in range (0, len(Ds)):
pitch = y * np.cos(np.radians(tilt))+Ds[dd]
# irr_Coffee_ch_1.8_xgap_0.6_tilt_18_pitch_1.6_Front&Back.csv
sim_name = ('irr_Coffee'+'_ch_'+str(round(clearance_height,1))+
'_xgap_'+str(round(xgap,1))+\
'_tilt_'+str(round(tilt,1))+
'_pitch_'+str(round(pitch,1))+'_Front&Back.csv')
sim_name2 = ('irr_Coffee'+'_ch_'+str(round(clearance_height,1))+
'_xgap_'+str(round(xgap,1))+\
'_tilt_'+str(round(tilt,1))+
'_pitch_'+str(round(pitch,1))+'_Ground&Back.csv')
ch_all.append(clearance_height)
xgap_all.append(xgap)
tilt_all.append(tilt)
pitch_all.append(pitch)
data = pd.read_csv(os.path.join(resultsfolder, sim_name))
FrontIrrad.append(data['Wm2Front'].item())
RearIrrad.append(data['Wm2Back'].item())
data = pd.read_csv(os.path.join(resultsfolder, sim_name2))
GroundIrrad.append(data['Wm2Front'].item())
ch_all = pd.Series(ch_all, name='clearance_height')
xgap_all = pd.Series(xgap_all, name='xgap')
tilt_all = pd.Series(tilt_all, name='tilt')
pitch_all = pd.Series(pitch_all, name='pitch')
FrontIrrad = pd.Series(FrontIrrad, name='FrontIrrad')
RearIrrad = pd.Series(RearIrrad, name='RearIrrad')
GroundIrrad = pd.Series(GroundIrrad, name='GroundIrrad')
df = pd.concat([ch_all, xgap_all, tilt_all, pitch_all, FrontIrrad, RearIrrad, GroundIrrad], axis=1)
df
# ### Let's calculate some relevant metrics for irradiance
# In[ ]:
df[['GroundIrrad_percent_GHI']] = df[['GroundIrrad']]*100/puerto_Rico_YEAR
df['FrontIrrad_percent_GHI'] = df['FrontIrrad']*100/puerto_Rico_YEAR
df['RearIrrad_percent_GHI'] = df['RearIrrad']*100/puerto_Rico_YEAR
df['BifacialGain'] = df['RearIrrad']*0.65*100/df['FrontIrrad']
# In[ ]:
print(df['GroundIrrad_percent_GHI'].min())
print(df['GroundIrrad_percent_GHI'].max())
# <a id='step4'></a>
# ## 4. Plot results
# In[ ]:
import seaborn as sns
import matplotlib.pyplot as plt
# In[ ]:
tilts_l = list(df['tilt'].unique())
ch_l = list(df['clearance_height'].unique())
print(tilts_l)
print(ch_l)
# In[ ]:
for tilt in tilts_l:
for clearance_height in ch_l:
df2=df.loc[df['tilt']==tilts[1]]
df3 = df2.loc[df2['clearance_height']==clearance_heights[2]]
df3['pitch']=df3['pitch'].round(1)
df3['xgap']=df3['xgap'].round(1)
sns.set(font_scale=2)
table = df3.pivot('pitch', 'xgap', 'GroundIrrad_percent_GHI')
ax = sns.heatmap(table, cmap='hot', vmin = 50, vmax= 100, annot=True)
ax.invert_yaxis()
figtitle = 'Clearance Height ' + str(clearance_height/ft2m)+' ft, Tilt ' + str(tilt) + '$^\circ$'
plt.title(figtitle)
print(table)
plt.show()
# <a id='step5'></a>
# ## 5. Raytrace with Tree Geometry
# <a id='step5a'></a>
# ### Tree parameters
# In[ ]:
tree_albedo = 0.165 # Wikipedia [0.15-0.18]
trunk_x = 0.8 * ft2m
trunk_y = trunk_x
trunk_z = 1 * ft2m
tree_x = 3 * ft2m
tree_y = tree_x
tree_z = 4 * ft2m
# <a id='step5b'></a>
# ### Loop to Raytrace and Sample Irradiance at Each side of the Tree (N, S, E, W)
# In[ ]:
for ch in range (0, len(clearance_heights)):
clearance_height = clearance_heights[ch]
for xx in range (0, len(xgaps)):
xgap = xgaps[xx]
for tt in range (0, len(tilts)):
tilt = tilts[tt]
for dd in range (0, len(Ds)):
pitch = y * np.cos(np.radians(tilt))+Ds[dd]
sim_name = (sim_general_name+'_ch_'+str(round(clearance_height,1))+
'_xgap_'+str(round(xgap,1))+\
'_tilt_'+str(round(tilt,1))+
'_pitch_'+str(round(pitch,1)))
coffeeplant_x = (x+xgap)/2
coffeeplant_y = pitch
demo.makeModule(name=module_name, x=x, y=y, xgap = xgap)
sceneDict = {'tilt':tilt,'pitch':pitch,'clearance_height':clearance_height,'azimuth':azimuth, 'nMods': nMods, 'nRows': nRows}
scene = demo.makeScene(module=module_name,sceneDict=sceneDict, radname = sim_name)
# Appending the Trees here
text = ''
for ii in range(0,3):
coffeeplant_x = (x+xgap)/2 + (x+xgap)*ii
for jj in range(0,3):
coffeeplant_y = pitch/2 + pitch*jj
name = 'tree'+str(ii)+str(jj)
text += '\r\n! genrev Metal_Grey tube{}tree t*{} {} 32 | xform -t {} {} {}'.format('head'+str(ii)+str(jj),tree_z, tree_x/2.0,
-trunk_x/2.0 + coffeeplant_x,
-trunk_x/2.0 + coffeeplant_y, trunk_z)
text += '\r\n! genrev Metal_Grey tube{}tree t*{} {} 32 | xform -t {} {} 0'.format('trunk'+str(ii)+str(jj),trunk_z, trunk_x/2.0,
-trunk_x/2.0 + coffeeplant_x,
-trunk_x/2.0 + coffeeplant_y)
customObject = demo.makeCustomObject(name,text)
demo.appendtoScene(radfile=scene.radfiles, customObject=customObject, text="!xform -rz 0")
octfile = demo.makeOct(octname = demo.basename)
analysis = bifacial_radiance.AnalysisObj(octfile=octfile, name=sim_name)
ii = 1
jj = 1
coffeeplant_x = (x+xgap)/2 + (x+xgap)*ii
coffeeplant_y = pitch/2 + pitch*jj
frontscan, backscan = analysis.moduleAnalysis(scene=scene, sensorsy=1)
treescan_south = frontscan.copy()
treescan_north = frontscan.copy()
treescan_east = frontscan.copy()
treescan_west = frontscan.copy()
treescan_south['xstart'] = coffeeplant_x
treescan_south['ystart'] = coffeeplant_y - tree_x/2.0 - 0.05
treescan_south['zstart'] = tree_z
treescan_south['orient'] = '0 1 0'
treescan_north['xstart'] = coffeeplant_x
treescan_north['ystart'] = coffeeplant_y + tree_x/2.0 + 0.05
treescan_north['zstart'] = tree_z
treescan_north['orient'] = '0 -1 0'
treescan_east['xstart'] = coffeeplant_x + tree_x/2.0 + 0.05
treescan_east['ystart'] = coffeeplant_y
treescan_east['zstart'] = tree_z
treescan_east['orient'] = '-1 0 0'
treescan_west['xstart'] = coffeeplant_x - tree_x/2.0 - 0.05
treescan_west['ystart'] = coffeeplant_y
treescan_west['zstart'] = tree_z
treescan_west['orient'] = '1 0 0'
groundscan = frontscan.copy()
groundscan['xstart'] = coffeeplant_x
groundscan['ystart'] = coffeeplant_y
groundscan['zstart'] = 0.05
groundscan['orient'] = '0 0 -1'
analysis.analysis(octfile, name=sim_name+'_North&South', frontscan=treescan_north, backscan=treescan_south)
analysis.analysis(octfile, name=sim_name+'_East&West', frontscan=treescan_east, backscan=treescan_west)
# <a id='step5c'></a>
# ### Single simulation until MakeOct for Getting a PRETTY IMAGE
# In[ ]:
tree_albedo = 0.165 # Wikipedia [0.15-0.18]
trunk_x = 0.8 * ft2m
trunk_y = trunk_x
trunk_z = 1 * ft2m
tree_x = 3 * ft2m
tree_y = tree_x
tree_z = 4 * ft2m
clearance_height = clearance_heights[0]
xgap = xgaps[-1]
tilt = tilts[0]
pitch = y * np.cos(np.radians(tilt))+Ds[-1]
sim_name = (sim_general_name+'_ch_'+str(round(clearance_height,1))+
'_xgap_'+str(round(xgap,1))+\
'_tilt_'+str(round(tilt,1))+
'_pitch_'+str(round(pitch,1)))
demo = bifacial_radiance.RadianceObj(sim_name,str(testfolder))
demo.setGround(albedo)
demo.readWeatherFile(epwfile)
coffeeplant_x = (x+xgap)/2
coffeeplant_y = pitch
demo.gendaylit(4020)
demo.makeModule(name=module_name, x=x, y=y, xgap = xgap)
sceneDict = {'tilt':tilt,'pitch':pitch,'clearance_height':clearance_height,'azimuth':azimuth, 'nMods': nMods, 'nRows': nRows}
scene = demo.makeScene(module=module_name,sceneDict=sceneDict, radname = sim_name)
for ii in range(0,3):
coffeeplant_x = (x+xgap)/2 + (x+xgap)*ii
for jj in range(0,3):
coffeeplant_y = pitch/2 + pitch*jj
name = 'tree'+str(ii)+str(jj)
text = '! genrev litesoil tube{}tree t*{} {} 32 | xform -t {} {} {}'.format('head'+str(ii)+str(jj),tree_z, tree_x/2.0,
-trunk_x/2.0 + coffeeplant_x,
-trunk_x/2.0 + coffeeplant_y, trunk_z)
text += '\r\n! genrev litesoil tube{}tree t*{} {} 32 | xform -t {} {} 0'.format('trunk'+str(ii)+str(jj),trunk_z, trunk_x/2.0,
-trunk_x/2.0 + coffeeplant_x,
-trunk_x/2.0 + coffeeplant_y)
customObject = demo.makeCustomObject(name,text)
demo.appendtoScene(radfile=scene.radfiles, customObject=customObject, text="!xform -rz 0")
octfile = demo.makeOct(octname = demo.basename)
# ***Now you can view the Geometry by navigating on the terminal to the testfolder, and using the octfile name generated above***
#
# >rvu -vf views\front.vp -e .0265652 -vp 2 -21 2.5 -vd 0 1 0 Coffee_ch_1.8_xgap_1.2_tilt_18_pitch_2.2.oct
# <a id='step6'></a>
# ## 6. Compile Results Trees
# In[ ]:
# irr_Coffee_ch_1.8_xgap_0.6_tilt_18_pitch_1.6_Front&Back.csv
ch_all = []
xgap_all = []
tilt_all = []
pitch_all = []
NorthIrrad = []
SouthIrrad = []
EastIrrad = []
WestIrrad = []
ft2m = 0.3048
clearance_heights = np.array([6.0, 8.0, 10.0])* ft2m
xgaps = np.array([2, 3, 4]) * ft2m
Ds = np.array([2, 3, 4]) * ft2m # D is a variable that represents the spacing between rows, not-considering the collector areas.
tilts = [18, 10]
y = 1
for ch in range (0, len(clearance_heights)):
clearance_height = clearance_heights[ch]
for xx in range (0, len(xgaps)):
xgap = xgaps[xx]
for tt in range (0, len(tilts)):
tilt = tilts[tt]
for dd in range (0, len(Ds)):
pitch = y * np.cos(np.radians(tilt))+Ds[dd]
sim_name = ('irr_Coffee'+'_ch_'+str(round(clearance_height,1))+
'_xgap_'+str(round(xgap,1))+\
'_tilt_'+str(round(tilt,1))+
'_pitch_'+str(round(pitch,1))+'_North&South.csv')
sim_name2 = ('irr_Coffee'+'_ch_'+str(round(clearance_height,1))+
'_xgap_'+str(round(xgap,1))+\
'_tilt_'+str(round(tilt,1))+
'_pitch_'+str(round(pitch,1))+'_East&West.csv')
ch_all.append(clearance_height)
xgap_all.append(xgap)
tilt_all.append(tilt)
pitch_all.append(pitch)
data = pd.read_csv(os.path.join(resultsfolder, sim_name))
NorthIrrad.append(data['Wm2Front'].item())
SouthIrrad.append(data['Wm2Back'].item())
data = pd.read_csv(os.path.join(resultsfolder, sim_name2))
EastIrrad.append(data['Wm2Front'].item())
WestIrrad.append(data['Wm2Back'].item())
ch_all = pd.Series(ch_all, name='clearance_height')
xgap_all = pd.Series(xgap_all, name='xgap')
tilt_all = pd.Series(tilt_all, name='tilt')
pitch_all = pd.Series(pitch_all, name='pitch')
NorthIrrad = pd.Series(NorthIrrad, name='NorthIrrad')
SouthIrrad = pd.Series(SouthIrrad, name='SouthIrrad')
EastIrrad = pd.Series(EastIrrad, name='EastIrrad')
WestIrrad = pd.Series(WestIrrad, name='WestIrrad')
df = pd.concat([ch_all, xgap_all, tilt_all, pitch_all, NorthIrrad, SouthIrrad, EastIrrad, WestIrrad], axis=1)
df.to_csv(os.path.join(resultsfolder,'TREES.csv'))
# In[ ]:
trees = pd.read_csv(os.path.join(resultsfolder, 'TREES.csv'))
trees.tail()
# In[ ]:
trees['TreeIrrad_percent_GHI'] = trees[['NorthIrrad','SouthIrrad','EastIrrad','WestIrrad']].mean(axis=1)*100/puerto_Rico_YEAR
print(trees['TreeIrrad_percent_GHI'].min())
print(trees['TreeIrrad_percent_GHI'].max())
# <a id='step7'></a>
# ## 7. Plot
# In[ ]:
tilts_l = list(trees['tilt'].unique())
ch_l = list(trees['clearance_height'].unique())
print(tilts_l)
print(ch_l)
# In[ ]:
for tilt in tilts_l:
for clearance_height in ch_l:
df2=trees.loc[df['tilt']==tilts[1]]
df3 = df2.loc[df2['clearance_height']==clearance_heights[2]]
df3['pitch']=df3['pitch'].round(1)
df3['xgap']=df3['xgap'].round(1)
sns.set(font_scale=2)
table = df3.pivot('pitch', 'xgap', 'TreeIrrad_percent_GHI')
ax = sns.heatmap(table, cmap='hot', vmin = 22, vmax= 35, annot=True)
ax.invert_yaxis()
figtitle = 'Clearance Height ' + str(clearance_height/ft2m)+' ft, Tilt ' + str(tilt) + '$^\circ$'
plt.title(figtitle)
print(table)
plt.show()