Ladder Calculations

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We use the BGA ladder calculations to score each flight. These are described at www.aircross.co.uk/bgaladder/Rules.htm. These are the definitive rules, and at the time of writing (2003 season), that's what Glidex implements. However, our previous scoring program used a different set of BGA calculations, and there has been some confusion because we didn't realise that the BGA calculations had changed. There's no guarantee that this won't happen again.

The calculations for scoring a ladder flight are as follows.

• The parameters to the calculation are
  • Km = Flight distance, in Km
  • Min = Flight time, in Minutes
  • Si = Speed index, the aircraft handicap
• The calculation is performed in three stages
  • The factor for the flight is determined
    • Undeclared flights score 0.50
    • Incomplete flights score (distance achieved)/(distance declared)
    • Declared and complete flights score 1.10
    • If the flight has 4 or more legs, multilply any of the above by 0.80
  • The actual speed of the flight is
    As = (Km * 60) / Min
  • The handicapped speed of the flight is
    Hs = (As * 100) / Si
  • The score includes speed and distance points
    Score = factor * (Km * (4000 + ( As * Hs ))) / (Si * 20)
• An attempt to put that into words
  • Si is a penalty factor for better aircraft. It is a number in the region of 100 which is always used as a percentage. For example, an LAK12 at 105 has a 5% penalty compared to an LS8-15m at 100.
  • The factor is a bonus or penalty according to the details for the flight
  • Hs is the flight speed in kph, adjusted down by Si.
  • The distance points in the score are 2 points per km flown, adjusted down by Si.
  • The speed points in the score are the As times Hs, multiplied by the km flown, divided by 2000, adjusted down by Si.
  • For example, 200k in 2 hours in an LS8-15m (Si=100) gives Hs=100, distance points 400, speed points 1000, score 1400.
• We do the calculations to high precision and round the final score to the nearest integer. Rounding Hs (for example, 29.55kph and 30.45kph would both be rounded to 30kph) can cause a 3% error in Hs and over 5% in the final score. The BGA calculations make no mention of this.

The previous BGA calculations used Hs*Hs in the speed calculation, instead of As*Hs. The change gives much less of an advantage to aicraft well below 100, and much less of a disadvantage to aircraft well above 100.

Here are some examples of the effect of the scoring rules, calculated for seven different aircraft with handicaps between 85 and 115.

	100km	200km	300km	400km	500km
1 hour	85 927 90 840 95 765 100 700 105 644 110 595 115 552
2 hours	85 408 90 377 95 349 100 325 105 304 110 285 115 268	85 1855 90 1679 95 1529 100 1400 105 1288 110 1190 115 1104	85 5377 90 4833 95 4371 100 3975 105 3633 110 3335 115 3074
3 hours		85 1086 90 993 95 914 100 844 105 784 110 731 115 684	85 2782 90 2519 95 2294 100 2100 105 1932 110 1785 115 1656	85 5862 90 5278 95 4782 100 4356 105 3987 110 3666 115 3384	85 10788 90 9684 95 8747 100 7944 105 7251 110 6648 115 6121
4 hours		85 817 90 753 95 698 100 650 105 608 110 570 115 537	85 1874 90 1708 95 1566 100 1444 105 1337 110 1243 115 1160	85 3709 90 3358 95 3058 100 2800 105 2576 110 2380 115 2208	85 6583 90 5934 95 5381 100 4906 105 4495 110 4137 115 3823
5 hours		85 692 90 642 95 598 100 560 105 526 110 496 115 469	85 1453 90 1333 95 1230 100 1140 105 1061 110 992 115 930	85 2713 90 2469 95 2260 100 2080 105 1923 110 1785 115 1664	85 4637 90 4198 95 3823 100 3500 105 3220 110 2975 115 2760
6 hours			85 1225 90 1130 95 1047 100 975 105 912 110 855 115 805	85 2171 90 1986 95 1827 100 1689 105 1568 110 1462 115 1368	85 3579 90 3254 95 2976 100 2736 105 2527 110 2344 115 2182
7 hours			85 1087 90 1007 95 937 100 876 105 821 110 773 115 730	85 1845 90 1695 95 1566 100 1453 105 1354 110 1267 115 1189	85 2942 90 2686 95 2466 100 2276 105 2109 110 1963 115 1834

Here are the equivalent scores with the previous calculations. All the scores with the new calculations have been pulled towards the average.

	100km	200km	300km	400km	500km
1 hour	85 1049 90 908 95 794 100 700 105 622 110 557 115 503
2 hours	85 439 90 394 95 356 100 325 105 298 110 276 115 256	85 2099 90 1816 95 1587 100 1400 105 1245 110 1115 115 1005	85 6202 90 5296 95 4568 100 3975 105 3487 110 3081 115 2741
3 hours		85 1194 90 1054 95 939 100 844 105 765 110 698 115 640	85 3148 90 2724 95 2381 100 2100 105 1867 110 1672 115 1508	85 6731 90 5766 95 4989 100 4356 105 3833 110 3399 115 3033	85 12484 90 10637 95 9152 100 7944 105 6951 110 6127 115 5436
4 hours		85 878 90 787 95 713 100 650 105 597 110 551 115 512	85 2080 90 1824 95 1616 100 1444 105 1300 110 1179 115 1077	85 4198 90 3632 95 3175 100 2800 105 2490 110 2230 115 2011	85 7537 90 6469 95 5609 100 4906 105 4327 110 3844 115 3438
5 hours		85 731 90 664 95 608 100 560 105 519 110 484 115 453	85 1585 90 1407 95 1261 100 1140 105 1038 110 951 115 877	85 3025 90 2645 95 2335 100 2080 105 1868 110 1689 115 1537	85 5247 90 4540 95 3969 100 3500 105 3112 110 2787 115 2513
6 hours			85 1317 90 1181 95 1069 100 975 105 895 110 827 115 768	85 2389 90 2108 95 1879 100 1689 105 1530 110 1395 115 1280	85 4003 90 3493 95 3078 100 2736 105 2452 110 2213 115 2011
7 hours			85 1155 90 1045 95 953 100 876 105 809 110 752 115 703	85 2005 90 1785 95 1604 100 1453 105 1326 110 1218 115 1125	85 3253 90 2861 95 2540 100 2276 105 2054 110 1867 115 1708