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FSH 2409.27 - 3P LOG SCALING
HANDBOOK
Denver, Colorado
Region 2 Amendment No. 11
July 1987
Page Code
33.1--1-4
33.1--1-6
34.4--1-5
35--1-2
36--1-2
Digest:
Superseded New
(Number of Sheets)
2
-
-
1
1
-
-
3
3
1
Provides procedures for use of automated data program. Removes Section 35 -
Accountability. Material now covered in FSH
2409.15, Timber Sale Administration
Handbook.
GARY E. CARGILL
Regional Forester

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33 OBTAINING RANDOM INTEGERS
After the sample load frequency has been determined, an estimate of the approximate number of logs per sample load is made, based on the best knowledge you have of the trees to be cut and size of trucks to be used. This estimate is needed for determining the population from which the 3P sample will be taken. Samples are then selected with the use of a specially prepared list of random integers.
A list of random integers or random numbers must be used for each separate sample. The numbers will be generated by a computer program on the basis of the number of samples needed to obtain a desired sampling error. These numbers will be developed on the scalers coefficient of variation (scaler's ability to hold constant the ratio of measured gross volume to predicted gross volume).
Numbers must be ordered on form R2-2430-
19, (see sec. 33.2 ex. 01), or directly through the Forest terminal using PROGRAM RAND.
The HP71B AUTOMATED SCALING
PROGRAM will generate its own random numbers.
33.1 - Information Needed for Ordering
Random Numbers.

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The HP71B AUTOMATED SCALING
PROGRAM generates its own random numbers. KZ is the only information needed for the program.
1. LIM. This is the amount of numbers needed to sample the sample loads. LIM can be computed by taking the total number of loads in the sale divided by the sample load frequency, times the average number of logs per load.
T = __ N = 50 5000
X f 10
N = Total number of loads in the sale = 5,000 f = Sample load frequency = 1-10 n = Number of sample loads to be scaled= 500 x = Average number of live logs per load= 50
T = Estimated total number of live logs in sample loads = 25,000
(Increase the estimated number of logs by
15%: 25,000 x 1.15 = 28,750 Numbers come in groups of 500 so round up to the next 500)
LIM = 29,000
Separate random numbers will not be necessary for dead.

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2. K. This is the gross volume of the largest log expected to be sampled. A log is considered as one log regardless of how many segments it contains. The value of (K) must be given much consideration as logs larger than the value of (K) are sure-to-be-measured; therefore, the occurrence of these large logs increases scaling time and scaling costs.
There should not be over 3 percent of the logs larger than the value of K.
To determine the value of K estimate the longest length log that the purchaser normally hauls, then use cruise summaries to determine estimated volume of the largest log based on these two variables using volume tables provided with the cruise. If cruise data is not available use the scaling experience of adjoining sales or similar sales.
Determining K is necessary for determining the KZ for the HP71B AUTOMATED
SCALING PROGRAM but K is not used, at the present time, in the HP71B AUTOMATED
SCALING PROGRAM. (See ex. 01 for calculating the KZ for the HP71B
AUTOMATED SCALING PROGRAM).
3. KZ. The value given "KZ" determines the sampling frequency; and is the total of all predictions, divided by the number of samples desired. Example: The KZ value = 500 board

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Page 5 of 16 feet (the slash is the last digit in Scribner and it is dropped to make Scribner Decimal C); this means that throughout the sale there would be a sample log in about every 500 board feet estimated (KPI's). The KZ value must always be greater than or equal to the value of K.
The objective is to sample about 10 percent of the sawlogs; therefore the KZ should always be 500 unless the value of K is larger than
500, and if so, then the KZ should be raised accordingly.
EXAMPLE:
K
100 - 500
KZ
500 - 750
750 - 1000
500
750
1000
If it is clear after scaling 3 sample loads, or at the end of the quarter, that there are definitely not enough sample logs, or too many sample logs, the KZ and/or the K should be adjusted to correct the under or over sampling. This should only be done before the
4th load is scaled or at the end of the quarter.
This is a standard guide for 3P sample log scaling. Form R2-2430-19, item #6, does not

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Page 6 of 16 apply when ordering random numbers for log scaling. Scalers should start out 3P scaling with a KZ of 500 when possible.
When this information is available, form R2-
2430-19 can be completed following the instructions on the form.
By leaving the third digit off both K and KZ, random numbers will be obtained in Scribner
Decimal C (rounded to the nearest ten).
Otherwise, the scaler will have to round off the last digit as he scales, which is time consuming. Predictions are made in Scribner
Decimal C; therefore, random numbers should be ordered accordingly. (See sec. 33.2, ex. 01).
Numbers should be ordered so that there is a minimum of approximately 10 sample logs per load for new 3P scalers. As the scaler develops an acceptable coefficient of variation, and acquires experience, the number of samples needed should decrease to approximately 10 percent of the logs in the load.
Each sale will need a set of random numbers generated specifically for an individual sale.
Random numbers should never be used on a sale other than the one they were ordered for.

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33.1 - Exhibit 1
The following is an example on how to compute K and KZ.
Timber sale = BIRD
Purchaser = JOE
(THIS IS THE LARGEST LOG IN THE
CRUISE DATA.)
BOARD FOOT LOG AND TREE REPORT.
******************************************
LENGTH FT. DIB.IN. BOARD FOOT VOLUME
SCRIBNER
12.0
16.5
16.5
16.5
16.5
16.5
.0
6.0
9.2
13.7
17.1
18.4
22.4
38.6
8.4
44.8
166.5
193.4
227.6
348.5
.0
******************************************
DBH.31.5
Joe historically hauls 33 foot logs, therefore, the volume of the bottom two segments is what we should use. 227.6 + 348.5 = 576.1 rounded to the nearest 10 and drop the last 0 to make 58 Scribner Decimal C.

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K should be 58 and KZ should be 75 for the
BIRD TIMBER SALE.

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8. At the bottom of the scale sheet, the sample log number is recorded. Then, the net
YI is divided by the gross KPI and carried to 4 decimal places for the ratio. Occasionally, a sample log with a gross KPI when scaled will be a cull with a net YI of zero. In order to have a ratio for this log and properly reduce the net volume, a ratio of 0.0000 will be entered, and the log will be counted in the numnber of samples.
34.4 - Scaling Procedures when using the
HP71B AUTOMATED SCALING PROGRAM
5
6
7
8
9
1
2
3
4
At the beginning of each load the scaler will enter the necessary information asked for by the HP71B AUTOMATED SCALING
PROGRAM (A.S.P.). When asked to enter the
POL (products other than logs) KZ, if scaling
POL enter the POL KZ (for example 6.66).
Then it will ask for the unit of measure.
Enter the number from the following table:
Scribner
Huber Cu. Ft.
Smalian Cu Ft.
Piece
Ton
Ln Ft.
PAM (per acre material)
Black Hills Cords (Supplement #21)
Black Hills Cords (Supplement #59)

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X To cross out a line - the line will still be printed on all reports but will not be included in any of the computations.
Random numbers are generated on the
HP71B for sawlogs and POL individually.
POL random numbers will be used for Black
Hills supplements 21, 59, and 87.
As soon as all the load information is entered the scaler will make the gross volume predictions (KPI) from the top end of each log going clockwise around the load.
For logs with POL attached, the scaler will make the prediction for the POL segment first, then make the prediction on the sawlog portion of the log.
OBJECTIVE: To 3P sample 10 percent of the sawlogs and 2 percent of the POL with every piece having a chance of being sampled.
Only logs or portions of logs designated as a
3P sample will be scaled.
The ratio must be of the same species or product as the KPI of the piece designated to be 3P sampled.

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If a prediction is made of either sawlog or POL volume, then when scaled the log or portions thereof is of a different product than the KPI, the scaled volume will be entered for the product of the KPI, then a prediction will be made for the correct product.
EXAMPLE 1: KPI for sawlog, but when scaled is POL
KPI Yl
2 for sawlog 0 for sawlog enter "0" for sawlog volume
Ratio - 0.0000 for sawlog
Then enter a KPI and random number for
POL.
EXAMPLE 2: KPI for sawlog, but when scaled a portion is sawlog and a portion is
POL.
KPI
2 for sawlog
Yl
1 for sawlog enter 1 for sawlog volume
Ratio - 0.5000 for sawlog
Then enter a KPI and random number for the balance of the log as POL.
EXAMPLE 3: KPI for POL, but when scaled is sawlog
KPI Yl

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2.66 for POL enter "0" for POL volume
0 for POL
Ratio - 0.0000 for POL
Then enter a KPI and random number for sawlog.
EXAMPLE 4: KPI for POL, but when scaled a portion is POL and a portion is sawlog
KPI
2.66 for POL
Yl
1.33 for POL enter 1.33 for POL volume
Ratio - 0.5000
Then enter a KPI and random number for the balance of the log as sawlog.
When dead is a different price differential from live.
EXAMPLE 5: KPI for live sawlog, but when scaled is classified as dead
KPI
30
Ratio - 0.0000
Yl
0 enter "0" for the live species volume
Then enter a KPI and random number for dead sawlog.
EXAMPLE 6: KPI for dead sawlog, but when scaled is classified as a live sawlog

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KPI
40
Yl
0 enter "0" for the dead volume
Ratio - 0.0000
Then enter a KPI and random number for the proper species, live sawlog.
When a sample comes up the scaler will stop making the KPI predictions and scale the log.
After the sample log is scaled the scaler will continue making KPI predictions and scaling the sample logs until the load is completed.
When the load is completed it is necessary to run an edit. This is done by pressing the edit key and making the necessary corrections.
After the edit on the load is completed and all corrections made, the scaler presses "load complete". The file number will be the sale brand plus the log load receipt number. (For example if the sale brand for the sale is FW and the log load receipt number si 456123, the scaler would enter FW456123).
When logs are encountered in the 3P sample that have a KPI of less that 1, such as a log 8 feet long with a 6" diameter top and scales .5
(Dec. C), the scaler will enter the volume as .5.
The HP71B SCALING PROGRAM generates

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After the scaler gets done scaling the loads for the day, the data will be transferred onto a cassette tape. The cassette tape, with the sample loads, will be kept for check scaling purposes until all the sample loads that are on the tape have been removed from the scaling area, then the cassette can be erased.
At the end of the day or, as soon as possible, the scaler or clerk will print out a report on each scale load, and make the necessary copies (for the mill, records, S.O. etc.). The scaler will need to audit the printout to check for errors not found in the edit.
The HP71B program report will extend volume and print a ratio and frequency factor for each sample (sawlog, POL on Black Hills supplements 21, 59, and 87). This information will be transferred to the load summary sheets (R2-2440-20) until the total program is automated. For an interim period, the total number of pieces per load will be erroneous due to duplicating logs. 5" DIB to 6" DIB occasionally cause classification problems when predicting the KPI. The sum or the KPI volume of samples of which the KPI was incorrectly classified will be adjusted down.
The minute volume ignored will be

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Occasionally a load will have a KPI volume of either sawlogs or POL without a sample. In this case the KPI volume will be the net volume for the load. This KPI volume will be adjusted with samples through the sample population for the period.
Refer to the HP71B AUTOMATED SCALING
PROGRAM handbook for more detailed instructions.
36 Check Scaling
Check scaling is the inspection of a scaler's work to determine the accuracy and proficiency of the scaler and, as such, is a necessary and important part of all Forest
Service volume determinations. Check scaling as described herein is different than normal check scaling.
The Regional Check Scaler will be responsible for scaler certification. The Regional and Zone
Check Scalers will make all check scales necessary for certifying scalers and for assuring continued qualification of these certified scalers. The Forest Supervisor is responsible for providing check scaling to

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Check Scaler.
The Regional and Zone Check Scalers will work under the general supervision of the
Forest Supervisor when working on the
Forest.
Frequency standards are related to the scaler rather than to an individual sale. They will be further related to scaler proficiency.
The minimum number of logs that will be considered for an adequate check scale is 35 plus the "K" logs.
The check scale will consist of the following:
The total number of pieces will be checked.
The number of pieces by species will be checked.
The sample logs plus "K" will be scaled.
The random number sheet that matches the load being check scaled will be checked to make sure the logs that should be 3P samples are 3P samples.
The Check Scale Report will be computed as follows: