Live Oak Crown Volumes Edward Frank February 27, 2009

ENTS,

A recent problem example, Problem #11, presented by Bob Leveret, at Ed Frank's behest, discussed the idea of calculating the volume of the top portion of a sphere.  In the example cited initially it modeled the canopy of some of the low and broad spreading live oaks that Larry Tucei had measured  Ed Frank’s description that motivates the above drawing follows. “Think of the hemisphere partially buried in the ground.  The shape of the tree canopy is the part that is sticking out.  There is a height h1 which is the height of the part sticking out of the ground.  In a tree this is the height of the tree.  h1 = R- h2   There is also r1 which is the pseudo- radius of the hemisphere at the point it intersects the ground surface as measured from the center of the circle at ground level to the edge of the circle.  This is the crown spread divided by two.”     The portion above the brown line is the area of interest, i.e the part of the hemisphere above ground. The volume of the area above the brown line is what we want to determine.  Bob Leverett produced a spreadsheet that automatically calculated the volume of this are based upon height of the tree and crown radius.  A tree crown fits this shape model if:   a) it has a domed shaped top surface, b) the base of the crown is flat or at ground level on a flat surface, and 3) the width of the crown spread is greater than or equal to twice the vertical thickness of the crown.

A number of trees measured by Larry Tucei as part of the Live Oak Project generally fit these shape parameters.  Nine examples were selected based upon photographs that showed the entire canopy form for testing this methodology.  The results are presented below.  The calculated crown volumes are presented in cubic feet.  These were calculated based upon maximum crown spread.  Average maximum crown spread would result is smaller volumes.

 Name Height (ft) Crown Spread (feet) Crown Volume (ft3) Walkaih Bluff Oak 73 165 984149 Josephine Stewart Oak 74.6 156 930309 Tree of Life 58.6 165 731870 Celina P. Roman Oak 69 135 665836 E. O. Hunt Live Oak 45 170 658418 Ruskin Live Oak 57 153 620950 Seven Sisters (multi) 57 153 620950 East Biloxi Live Oak 57 144 561118 Shrine of the Holy Cross Oak #1 75 (65a) 124.5 (a 539444) McDonogh Oak 48.9 154.5 519605 Sarah Hunt Oak 51 136.5 442616 Middleton Oak 67.5 (59a) 118 (a 430135) Edgewater Park Oak 47 120 320140

Looking at the results you can see that by far the largest volume crown measured was for a live oak the Walkaih Bluff Oak at almost 900,000 cubic feet.  The Middleton Oak, one of the largest volume trunk live oaks known, and certainly the largest ever accurately modeled, finished eighth out of nine trees calculated.  Other live oaks have either a more typical upright trunk form, or for this initial calculation set did not have photographs of the full crown  showing it form.  More will be added as the canopy forms of trees on the list are reviewed. many of the other live oaks measured will also fit into this form category.  All photos are by Larry Tucei, except for the Middleton Live Oak photo by Will Blozan.

Report by Edward Frank and Larry Tucei

Ruskin Live Oak in Ocean Springs, Ms. 27'2" cbh, 57’ height  and 153' Spread http://www.nativetreesociety.org/fieldtrips/mississippi/liveoakjan2007/ms_live_oaks.htm

 r1 h1 R Vq 76.5 57 79.83553 620950

East Biloxi Live Oak 35' CBH  57' Height 144' Spread http://www.nativetreesociety.org/fieldtrips/mississippi/liveoakjan2007/ms_live_oaks.htm

 r1 h1 R Vq 72 57 73.97368 561118

*** E.O. Hunt Oak, located at the South Ms. Regional Center in Long Beach, CBH- 37', Spread-170' and Height ~45' http://www.nativetreesociety.org/fieldtrips/mississippi/liveoak/live_oak_galleries.htm

 r1 h1 R Vq 85 45 102.7778 558418

*** The Sara Hunt Oak, also located at the South Ms. Regional Center- CBH-26'7", Spread-136.5, Height ~51' http://www.nativetreesociety.org/fieldtrips/mississippi/liveoak/live_oak_galleries.htm

 r1 h1 R h2 V Vp Vq 68.25 51 71.16728 442616

*** Edgewater Park Oak. CBH-22'11", Spread-120' and Height 47'   http://www.nativetreesociety.org/fieldtrips/mississippi/edgewater/edgewater_mall_live_oak.htm

 r1 h1 R h2 V Vp Vq 60 47 61.79787 320140

*** Tree of Life, Audubon Park, New Orleans.- CBH-35’ 2”, Spread-165’ http://www.nativetreesociety.org/fieldtrips/louisiana/audubon/audubon_park_live_oaks.htm

There has been a limb breakage and the maximum spread now is 150 feet.  A remeasure may yeild a higher value.

 r1 h1 R h2 V Vp Vq 82.5 58.6 87.37381 731870

Dedeaux Oak located at 5607 Vidilia Rd., Delisle, MS- CBH-30’1”, Spread-148’ and Height-69’. http://www.nativetreesociety.org/fieldtrips/mississippi/delisle/delisle_and_pass_christian.htm

 r1 h1 R Vq 74 69 74.18116 765523

*** Celina P. Roman Oak, CBH-25', Height-69' and Spread-135 http://www.nativetreesociety.org/fieldtrips/louisiana/oak_alley/oak_alley_plantation.htm

Limb breakage has reduced the spread to 112.5

 r1 h1 R Vq 67.5 69 67.5163 665836

McDonogh Oak, CBH-27'7", Height-48.9' and Max. Spread- 154.5' http://www.nativetreesociety.org/fieldtrips/louisiana/citypark/city_park_new_orleans_louisiana.htm

 r1 h1 R Vq 77.25 48.9 85.46802 519605

Seven Sisters Live Oak – Multitrunk CBH- 47' 9", Height-57' and Spread-153'. http://www.nativetreesociety.org/fieldtrips/louisiana/sevensisters/seven_sisters_live_oak.htm Multitrunk tree with seven trunks - volume is of composite crown.

 r1 h1 R Vq 76.5 57 79.83553 620950

Shrine of the Holy Cross Oak #1, CBH- 22'7", Height-75', Spread-124.5'. http://www.nativetreesociety.org/fieldtrips/alabama/knollpark/andrew_jackson_oak_and_knoll_park.htm  (base of canopy at about 10 feet)

 r1 h1 R Vq 62.25 75 63.33375 677413 62.25 65 62.30817 539444

Middleton Oak, SC  CBH 32.8 feet, height 67.5, spread 118 http://www.nativetreesociety.org/fieldtrips/south_carolina/middeltonoak/middelton.htm  Does BVP have any crown volume calculations?  I used the measured height of 69 feet and also used 59 feet for height to offset the small point sticking out of the main mass of the canopy.  The latter results in a full hemisphere.  Number calculated for comparison purposes.

 r1 h1 R Vq 59 67.5 59.53519 530117 59 59 59 430145

Walkaih Bluff Oak H-73' Sp-165'.

 r1 h1 R h2 V Vp Vq 82.5 73 83.11815 984149

 r1 h1 R h2 V Vp Vq 78 74.6 78.07748 930309

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Eastern Native Tree Society http://www.nativetreesociety.org
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PDF of the Document measure/volume/liveoakcrown.pdf

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