(11C) Tree Heights

[Dieter]

(11-03-2018 01:35 AM)Gamo Wrote:  Dieter thanks for the better program update.

See below. ;-)

(11-03-2018 01:35 AM)Gamo Wrote:  Personally I program this Tree Height as simple to operate as possible

Does it get simpler than entering the three values on the stack?

(11-03-2018 01:35 AM)Gamo Wrote:  so I put all input operation separately on each labels like so
[A] For Known Distance and Slope Tip
[B] For known Positive Slope Base
[C] For Known Negative Slope Base
[D] Compute Tree Height

Again: there is no need for separate calculations for positive or negative slope values. Try it: simply enter –20 at [B]. You may also use two separate labels for the distance and the slope percent to the tip.

Finally here is another version:

In many cases it is a good idea not to follow a given path but to try a new approach instead. This is also the case here. The tree height can also be calculated this way:

b = a·cos(B2) · tan(B1) – a·sin(B2)

The point here is that the sine and cosine term can be simultaneously calculated by means of the P–>R command. And the tangent simply is the tip slope divided by 100.

This leads to the following even shorter program:

Code:

01 LBL A
02 EEX
03 2
04 ÷
05 X<>Y
06 LstX
07 ÷
08 R↓
09 TANˉ¹
10 X<>Y
11 →R
12 R↑
13 x
14 X<>Y
15 -
16 RTN

And here is a version that uses the label keys:

Code:

01 LBL A
02 STO 1
03 RTN
04 LBL B
05 1
06 %
07 TANˉ¹
08 STO 2
09 R↓
10 RTN
11 LBL C
12 1
13 %
14 STO 3
15 R↓
16 RTN
17 LBL D
18 RCL 2
19 RCL 1
20 →R
21 RCL 3
22 x
23 X<>Y
24 -
25 RTN

f[USER]

Enter base distance [A]
Enter base slope percent [B]    (may be positive or negative)
Enter tip slope percent [C]
Calculate tree height with [D]

 56 [A] =>  56,00
 20 [B] =>  20,00
 40 [C] =>  40,00
     [D] =>  10,98

-20 [B] => -20,00
      [D] =>  32,95


Addendum:
I was playing around a bit with a TI59 emulator, so here also is a version for the TI58/59.

Code:

000 76  LBL
001 11   A
002 42  STO
003 01   01
004 92  RTN
005 76  LBL
006 12   B
007 53   (
008 24  CE
009 55   ÷
010 32  X⇄T
011 01   1
012 00   0
013 00   0
014 54   )
015 22  INV
016 30  TAN
017 42  STO
018 02   02
019 32  X⇄T
020 92  RTN
021 76  LBL
022 13   C
023 42  STO
024 03   03
025 92  RTN
026 76  LBL
027 14   D
028 53   (
029 43  RCL
030 01   01
031 32  X⇄T
032 43  RCL
033 02   02
034 37  P/R
035 94  +/-
036 85   +
037 32  X⇄T
038 65   x
039 43  RCL
040 03   03
041 55   ÷
042 01   1
043 00   0
044 00   0
045 54   )
046 58  FIX
047 02   02
048 52  EE
049 22  INV
050 52  EE
051 92  INV
052 58  FIX
053 92  RTN

Usage is the same as above.
The final steps round the result to two decimals.

Dieter