1. Oku losZ{k.k Ekkiu & 2 Ok`{kksa dh ÅapkbZ Ekkiu

2. Forest Mensuration bl l= dk mn~s’; izf’k{k.kkfFkZ;ksa dks ou ekiu ds ckjs fuEu dh tkudkjh nsuk gS % –ifjHkk"kk,a –mapkbZ ukius ds fl)kar –mapkbZ ukius ds midj.k Aims: The aim of this session is to help trainees in analysing the following aspects of Forest Mensuration: 1. Definitions 2. Height measurement principles 3. Instruments of height measurement

3. ifjHkk"kk,a Definitions dqy ÅapkbZ ¼VksVy gkbZV½ ;g t+ehu Lrj ls N= ds lcls maps fcUnq dh lh/kh nwjh gS A BwaB ÅapkbZ ¼ cksy gkbZV½ ;g t+ehu Lrj ls igys N= fuekZ.k djus okyh igyh thfor ;k e`r 'kk[kk dh nwjh gS A Total height: is the straight-line distance from the highest point of the crown to the ground level. Bole height: is the distance from the ground level to the position of the first crown forming living or dead branch.

4. ifjHkk"kk,a Definitions - 2 BwaB ÅapkbZ & BwaB dh t+ehu Lrj ls f’k[kj rd dh mapkbZ gS A N= yEckbZ& ;g og lh/kk uki gS tks N= ds f’k[kj ls ysdj ] BwaB dh lcls fupyh gjh 'kk[kk o fupyh gjh 'kk[kkvksa ftu ls gjk N= curk gS] ds e/; fcanq rd gS A N= ÅapkbZ & ;g tehu Lrj ls ysdj rus dh lcls fupyh gjh 'kk[kk o fupyh gjh 'kk[kkvksa ftu ls gjk N= curk gS] ds e/; fcanq rd dh mapkbZ gS A Stump height: is the height of the top of the stump above ground. Crown length: is the vertical measurement of the crown of a tree from the tip to the point half way between the lowest green branches forming green crown all round and the lowest green branch on the bole. Crown height: is height from the ground level to the point half way between the lowest green branches forming green crown all round and the lowest green branch on the bole.

6. mapkbZ ukius ds fl)kar Height measurement principles VªhxukseSfVªd fl)kar & VªhxukseSfVª xf.kr dh og 'kk[kk gS tks dks.kksa o f=Hkqtksa dh Hkqtkvksa ds uki o mu ij vk/kkfjr dk;ksZa ls lac/k j[krh gS A ftu rhu VªhxukseSfVªd dk;ksaZ ¼ lkbZu] dkslkbZu o VSUtsaV ½ ds lac/k esa ge ckr dj jgs gSa os f=Hkqt dh nks Hkqtkvksa dh yEckbZ dk vuqikr gS A ;s vuqikr,d dks.k ¼FkhVk½ ds,sls VªhxukseSfVªd dk;Z gSa ftlesa foijhr Hkqtk o`{k dh ÅapkbZ dks bafxr djrh gSA Trigonometric principle: Trigonometry is a branch of mathematics dealing with measurements of the angles and sides of triangles, and functions based on these measurements. The three basic trigonometric functions that we are concerned with here (sine, cosine, and tangent) are ratios of the lengths of two sides of a triangle. These ratios are the trigonometric functions of an angle, theta, such that here, opposite side (y) refers to tree height.

7. leku f=Hkqt ds fl)kar PRINCIPLE of SIMILAR TRIANGLES leku f=Hkqt os f=Hkqt gSa ftuds rr~LFkkuh dks.k rks leku gSa ijUrq ftudh rr~LFkkuh Hkqtk,a vyx yEckbZ dh gks ldrh gSa A Similar triangles are triangles whose corresponding angles are the same, but whose corresponding sides may be of different lengths.trianglesanglessideslengths Thus △ ABC is similar to △ DEF: f=Hkqt ABC f=Hkqt DEF ds leku gS ∠ ABC= ∠ DFF; ∠ BCA= ∠ EDF; ∠ CAB= ∠ DEF A B C D E F

8. leku f=Hkqt SIMILAR TRIANGLES - 2 AB / DE = AC / DF B A C D FE

9. leku f=Hkqt SIMILAR TRIANGLES - 3

10. vH;kl 1 Exercise 1 ;fn vki tkurs gSa fd nks f=Hkqt leku gSa rks vki lekurk dh ifjHkk"kk ds vk/kkj ij ;g Hkh izekf.kr dj ldrs gSa fd 1 f=Hkqtksa dh rr~LFkkuh Hkqtk,a vuqikfrd gSa vkSj 2 f=Hkqtksa ds rr~LFkkuh dks.k vuqdwy gSa A If you know two triangles are similar, you can use the definition of similarity to prove: 1.Corresponding sides of the triangles are proportional, and 2.Corresponding angles of the triangles are congruent

11. If the tree’s shadow is 50’ long & the woman’s shadow is 10’ long; how tall is the tree if the woman is 6’ tall? vxj isM+ dh Nk;k 50 QhV yEch gS vkSj efgyk dh 10 QhV rks isM+ fdruk mapk gS ;fn efgyk 6 QhV yach gS

12. leku f=Hkqtksa ds fl)kar ij vk/kkfjr midj.k Instruments based on properties of similar triangles fØlfpu fgIlksehVj Christen's hypsometer fLeFkht+ fgIlksehVj Smythies' hypsometer mUur dSfyilZ Improved callipers

13. fØlfpu fgIlksehVj Christen’s Hypsometer

14. VªhxukseSfVªd fl)karksa ij vk/kkfjr midj.k Instruments based on trigonometric principles czSafMl fgIlksehVj Brandis hypsometer,cuht+ ysoy Abney's level gkxk vkYVhehVj Haga altimeter Cywe&yhl fgIlksehVj Blume-leiss hypsometer jSykLdksi Relaskop

15. Trignometric Principle VªhxukseSfVªd fl)kar

16. ,cuht+ ySoy Abney Level

17. ,cuht+ ySoy & dSls bLreky djsa ns[kus okyk isM+ ls nwj ml LFkku ij [kM+k gksrk gS tgka ls isM+ dh pksVh o ry nksuksa fn[kkbZ nsa A fQj vkbZihl fudkydj mlds fiugksy ls isM+ dh pksVh dks ns[kk tkrk gS A blls midj.k Vs<+k gks tkrk gS 'kh’ks esa cqycqyk ugha fn[kkbZ nsrk gSA blfy, isM+ dh pksVh ns[krs le; isp dks ?kqek;k tkrk gS rkfd fLifjV ysoy {kSfrt voLFkk esa vk tk, A fLifjV ysoy dks yxkrkj /khjs /khjs fgykdj ml fLFkfr esa yk;k tkrk gS tc cqycqys dh Nfo dks {kSfrt rkj dh ykbZu 'kh’ks ij nks cjkcj Hkkxksa esa ckaVs vkSj nwljs fgLls esa isM+ dh pksVh {kSfrt rkj dks Nwrh fn[krh gks A bl fLFkfr esa isM+ dh pksVh ds mBku dk dks.k i<+ fy;k tkrk gS A blh rjg ry ds <yku dk dks.k i<+ fy;k tkrk gS A fQj mi;qDr QkZewys ds ek/;e ls isM+ dh mapkbZ fudkyh tkrh gS A

18. Abney Level – How to use? The observer stands away from the tree at a place from where the top of the tree and the base are visible. Then the top of the tree is sighted through the pine hole of the eyepiece after pulling it out. This makes the instrument inclined and the bubble is not seen in the mirror. Therefore, while sighting the top, the screw is Rotated to bring the spirit level in a horizontal position. The spirit level is continued to be moved slowly to the position when the bubble image is bisected by the line of horizontal wire on the mirror and in the other half the tree top is seen touching the horizontal wire. At this position, angle of elevation to the top of the tree is read. Similarly, the angle of depression to the base can also be read and the height of the tree determined by using suitable formulae

19. ,cuht+ ysoy,cuht+ ySoy ds ykHk : 1ouhZ;j ds lkFk mBku o <yku ds lVhd dks.k nsrk gS A 2NksVk o gYdk gS vkSj igkM+ksa esa vklkuh ls bLrseky fd;k tk ldrk gS A,cuht+ ySoy dh gkfu % 1 gkFkksa dh daiu ls isM+ dh pksVh ;k ry dks ns[kuk FkksM+k eqf’dy o le; yxus okyk gS A 2 LihfjV ySoy dks isp fgykus ds lkFk isM+ dh pksVh ;k ry dks ns[kuk o,SMtLV djuk ] Fkdkus okyk dk;Z gS A

20. Abney Level Advantages : 1.Gives accurate angles of elevation or depression with the vernier 2.Small and light and can be used even in hills without difficulty. Disadvantages: 1.Shaking of the hand makes the sighting of the top or bottom of the tree a little difficult and time-consuming 2.The spirit level has to be adjusted by moving the head of the screw while simultaneously looking to the top or bottom of the tree. This is quite tiresome.

21. Cywe&yhl fgIlksehVj Blume Leiss Hypsometer

22. gkxk vkYVhehVj Haga Altimeter

23. vH;kl&2 Økmu gkbZV dk D;k eryc gS\ mapkbZ ukius ds fl)karksa dk fooj.k nks A isM+ dh mapkbZ ukius ds fy, VSatSaV eSFkM dk fooj.k nks A mapkbZ ukius ds midj.kksa dh lwph nsa A,scht+ ySoy ds ckjs esa o ykHk & gkfu ds ckjs esa fy[ksa A leku f=Hkqtksa ls vki D;k le>rs gSa \

24. Exercise - 2 What do you mean by crown height? Describe the height measurement principles. Describe the height measurement of a tree by using tangent method. List the instruments of height measurement? Describe the Abney's Level, its advantages and disadvantages. What do you understand by Similar Triangles?

25. THANK YOU /kU;okn