forest maturation 20. here is that final lecture for the tree form factor where i'll tell about the form factor and how to calculate the form factor from height so tree form already i told you this is defined as the rate of temperness of a log or stem how what is the rate of tapernace from the base to the top you can see here the taperness is very less it is cylindrical here it is a parabolic here it is a cone it is irregular and how to calculate the tree form that is very important is defined as the ratio of the volume of a tree to the volume of a cylinder having the same length and cross section you can see this is the tree which is having this height and we have considered this as a same cross-sectional area from the top to the below so what is the ratio ratio of what you can see this is the volume of a cylinder exact volume of a cylinder it is compared this volume of cylinder with the shape of a tree so tree is like this we can see so ratio of the volume of a tree this volume of a tree to the cylinder this is cylinder having the same length the same length this is the same length same length and the same cross section now this you can see this 2 is compared with the cross section of this one this is here over estimate extra and this is underestimate less so this is not there in your tree this volume is not included this part and this is extra here so when we see we will consider this entire tree with this cylinder then it is underestimate means the volume will be more but it is less because we are considering some dia somewhere here okay this same dial we are taking here so form factor what is the form factor we'll see the ratio what is the ratio so ratio will start from zero to one okay so it will be zero point twenty zero point thirty zero point forty and so on so and so so as it approaches to one it will be cylinder approaches to one it will be cylinder we should know about form factor then only we can know how much you have the actual volume in a tree this is artificial form factor so most commonly used in india is artificial form factor and artificial form factor is we take it at dbh or we also call it breast height form factor we take at the breast height this at the breast height we will take as form factor is defined as a ratio of the volume of a tree to the volume of the cylinder of the same length and same cross sectional area the artificial form factor also called as breast height form factor because we take the basal area at brush height so the measurement what we will be taking here the reference is the breast height form factor breast height is a fixed measurement point so we take the cross-sectional area or diameter and at the breast height so this is the breast height 1.37 meter from the ground level here we take the dia and the volume refers to the whole tree that is above the point of measurement at breast height and also below the point of measurement from the breast height so it is not very reliable as a form factor but because different trees pieces with different height may have a same form but it is being more used just because of the very handy measurement and easy for the computation of the cross sectional area at diameter at best height so this is artificial form factor so we will consider volume of a full length of the full height of the tree from the breast let's calculate this breast height form factor or artificial form factor we also say is f is equal to v over s h we use the volume of a tree in cubic units what is the volume of water in a cubic units as is the cross sectional area or basal area this cross sectional area or a basal area here okay and height is the height of a tree so this is the formula for calculating the artificial form factor so how will calculate it let's have the value if you have a volume this is 3.26 let's take the volume of 3.26 the entire volume is 3.26 okay then basal area we'll calculate by this diameter pi d square over 4 diameter we are getting how much diameter we are getting 48 centimeter will convert into meter that is 0.48 meter okay because we need in cubic meter we need in cubic meter so uh pi into d square over 4 this is 3.142 is pi into 0.48 this value of putting we are getting the this sectional area or basal area sectional area or basal area we are getting this volume 0.1809 meters square meter then height is 30 already given will fit this into this formula will fit in this formula v over sh v is the volume volume we this is the volume we are getting 3.26 and s is equal to sectional area just now we have calculated this one 0.1809 into 30 is the height of a tree we get somewhere the uh form factor of 0.60 lacquer so we get a shape of a parabolic here so this is a shape we can say this is a form class ah let's understand about the shape of a tree or equal a form factor so when we talk of form class we'll understand about this is a range this is the different range you can see the range range is point three two five two point three seven five we get this kneeler shape and when we go to point four seven two point five two we got a connect shape then we when we have a point seven five two point seven two range we get a quadratic parabola and when we go up to point seven seven five two point eight two five we get a cubic parabolic so when we reach one it is a cylindrical so the greater the taperness small is the form factor so greater the taperness you see the smaller the form factor will be here next is absolute form factor convenient instead of bending here we are taking here it is not a breast height at any convenient height we get the nexus absolute form factor with the reference to the cylinder absolute form factor is what at a convenient height will take a day at any con at convenient height we'll take okay wherever we feel convenient so if you feel here uh it is more what you say uh buttressing here we can take it this height and then but this is considered from where we will take the basal area from that point to the top we will consider the as with the cylinder okay with reference to the cylinder will take a volume so if you take at the base we will consider the full tree as a cylinder if you take at this level we will take it from above from this point so this is absolute form factor absolute form factor in absolute form factor we measure the basal area at any convenient height of a tree we may take the basal area or diameter at the lower portion we can come more at the lower also avoiding the stump we can come at any convenient because here we are finding it is a very cylindrical tree but we consider we refer the volume of a tree from above from the point of measurement either we take at any convenient height we may take at this height we may take at more lower we can come at more lower at the base avoiding the stump and then we will refer the volume of a tree above the point of measurement to the top of the tree so this is absolute form factor so normal or true form factor this normal and true form factor is measured at constant proportion of height so we will take the entire height from up here to here and that will measure the height how much height it is then we will take by one tenth of that measurement here we'll take that cross sectional year we will take the cross sectional year we will take the cross section and that tree will take the cross this is measured at the constant portion of the total height question percent or we can say one tenth also we can say or we can say one twentieth also we can take so it depends now we'll take the full length then we'll decide one tenth one to hit ten percent twenty percent like this but we have to take the dia at the entire length so it is the calculation of the volume of full tree we will get the exact volume but it is a destructive sampling or it is very difficult to go from lower to that upper one and time consuming that's why in india we take breast height form factor so form height what is foam height so form height is used to determine how far it is reasonable to assume the volume which is proportional to basal area how far the volume is proportional to this basal area we will understand this one so the form height remains constant with increasing diameter so we have to understand this is very important this form height remains constant it should remain constant with increasing diameter so form height is defined as the product of form factor and the total height of a tree okay so what is form height we will uh see this one two diagrams are there we see two diagrams are there for example this is a diode of 50 centimeter it increased to 55 centimeter it increases 60 centimeter similar 50 centimeter 55 centimeter 60 centimeter form height is used to determine how far it is reasonable to assume the volume is proportional to the area now how much if the volume is proportional to the basal area okay now we see suppose this is a tree this is the basal area this is the basal area it is increasing slowly slowly but height is not increasing so it is not reasonable to assume that the volume is proportional to the vaseline area so if you see this one the cross-sectional area is increasing slowly slowly like 50 to 55 centimeters 60 centimeter even the height is also increasing as this basal area is proportional or the volume we can say volume is proportional to the basal area this entire volume is here this entire volume is related to 50 centimeter here this entire volume is related to 55 centimeter here and and then this entire volume is related to 60 centimeter here as the diameter is growing up even your tree height is coming up and the volume has been increasing so when the volume is proportional to basal area we say that form height is used it used to determine that how far it is reasonable how far it is reasonable you can think that the volume is proportional volume is proportional equal to the basal area so this means a form height so form quotient now that is next is form quotient what is form quotient so form quotient is defined as the ratio between the mid diameter and diameter between mean diameter and diameter what the ratio between mean diameter and diameter so this is the mid diameter and the diameter so let's understand this nicely about the their form quotient and then form quotient is been defined by two foresters first is australian forester shuffle other one is foolish forester tor johnson so what does ashiful says so if this is a tree full tree so he has made this form quotient as the mid diameter divided by diameter but his mid diameter is from the entire length if this is the entire length of a tree we take it at 50 here if this is somewhere 20 at 10 we will take it here so as per the schiffer the mid diameter is the half of the total tree here somewhere here so d square somewhere here half divided by this deviation okay so australian forester schiffer has defined the form quotient you can say we name it as a normal form quotient we call it normal form quotient so normal form question is the ratio between the mid diameter and the diameter the mid diameter is the diameter of the full total height of a tree and the divide the 50 percent here half of this one or fifty percent of the length of the height of the total tree this is called normal form question by schiffer but here by todd johnson he has made absolute form factor okay one is normal form factor another one is called absolute form factor this absolute form factor he has taken what he has taken d2 not from the base of a tree he has taken d2 from the dbh from the dbh he is made 50 here okay so it is halfway between the height and the total height halfway from the right and the total height is d2 here divided by d1 this is dbh so it is a ratio measuring the diameter at a height halfway between the height and the total height of a tree so this is called absolute form factor by tor jensen so there are two form factor one is normal form factor by shiful from he is taking the ah diameter of the total height half of the total height for tree and tor jason has taken from the height of the to the total height half of that one so this is the difference between normal form factor and absolute form factor so form question by two forester one is austrian forester that is shuffle and one by thor johnson so again let's go for the firm class already i told you form class is defined as one of the interval in which the range of form quotients of that is divided by classification as we use here so we classify like this also we we have taken the range suppose we are taking point three two five two point three seven five so at the mean of this one thirty five we are taking is shape is neil i told you that this is kneeling here so form factor more taperedness you could see more taperedness less form factor so similarly that taperedness is bit less form factor is also increasing in per cubic parabolic we can see it is 80 so this is cubic per hour light taper equations which is very important because it predicts the changing diameter along the tree stem over time in a or at a particular time it is over time or at a particular time so taper equation predicts the diameter at any point it produces the diameter at any point of the tree stem based on and total height of a tree to determine the stem profile or stem form now there are equations by uh hoja's formula let's see this hoses formula he says that d divided by dbh is equal to c log that is uh under bracket c plus l divided by c now let's see what is uh d d is the diameter this is the diameter at any point of this time any point of this time we can see here here here any any point of the stem from where we are taking an point that is called l l is the distance from the point from the top of the tree to the point of the d major if you are measuring d here l will be here if i imagine d here l will be here so at any point we are taking this d and c capital c and small c are constant for each form classes so we will put the value and we will get the houses formula so this taper equations help us to know predict the stem profiles in future how it grows whereas formula is also similar we call it d divided by dbh is equal to l divided by a into b d is a diameter at any point diameter at any point and a and b are the constant for form classes okay so these formulas have been calculated have been used for preparation of taper tables in western countries so what it helps in the preparations what professions of the taper tables in western countries these formulas help us okay so taper equations give helps us for the preparation the taper tables it helps us to make the taper tables and it predicts the changing diameter along the stem over time or at a particular time so there are two formulas hodges formula and varis formula what is the use of form factor that's important we should know what is the use of your form factor first is to estimate the volume of a standing tree this factor will tell us how to estimate the volume of a standing tree because taperness will give us less volume cylindrical will give us more volume it also help us to study the law of growth how the tree grows in the open area in the stand in the stand also how it competes with each other and how it becomes a cylindrical and how it grows like there's an example of tick which in myanmar forest is to grow in a closed stand because it's a light demanding due to its light demanding it grows and comes in the top of the canopy and becomes more cylindrical more in length so the quality of teak or the timber of the teak which we get from manipur forest is more valuable so it helps us to study the law of growth of such type of trees thank you very much to be with the lectures on tree form factor this tree form factor is very important for the calculation of volume because now as we know how to calculate the diameter by diameter we know how to calculate the cross sectional area we know how to calculate how to measure the height of a tree in a different area we get the three things one is the diameter for the diameter we make the cross sectional area we get the height of a tree as we get the height of a tree cross-sectional area and form factor we can have the volume of a tree we can have a volume of a stand and we can calculate the entire volume and make our volume tables also so there are two tables of volume one is called local volume table or general volume table and how to do that one will be going on that one in coming lectures thank you