CJA Images: The Longdin-Ward Effect

Regular Light & Land customers will be familiar with the time keeping challenges associated with each photo stop. Quite often a 10 minute stop turns into half an hour, or you return on time only to find that someone else is just setting up and you would have had time for that final image after all.

During the Lofoten Islands and Northern Norway trip in July 2007 I sat down with David Ward and Janneke Kroes to see if we could come up with some way of predicting this effect to assist tour leaders in setting times and managing the expectation of clients.

The initial analysis identified a number of factors that could affect the duration of each photo stop:

• The range of subjects available at a location: If there are too many options and not enough time, people will inevitably be late back. If there are a limited number of options, people are likely to be finished on time. If there are too few options then everyone will get in each other's way leading to the inevitable 'tripod rage' incidents and delays as people have to wait for others to finish.

• The changeable light: How often does the light change dramatically just as you are getting to the end of the time allocated? Most tour leaders will allow additional shooting time in these circumstances.

• Weather: Bad weather can sometimes curtail a stop, although some tour leaders are more inclined to keep on going than others.

• Large format photography: By its very nature, large format photography needs at least a 30 minute stop to be viable. On the positive side, LF photographers will not attempt to shoot at short stops so can be assured of being ready in time. On the downside, once a LF photographer starts setting up you can be sure that you won't be able to leave for another 20 minutes or more.

• Digital photography: Being limited only by the size of their memory cards, some digital photographers will just keep on taking pictures, losing track of time.

• Tour leader: A tour leader working on their own is likely to have more difficulty in keeping to time than a pair of leaders who are used to working together. However, having two leaders can cause conflict if they are not used to working together and there is a difference in opinion on timings and priorities.

After some deliberation, I determined that the key factors in the duration of each stop are the tour leader(s) and the types of client on the trip. All the other factors should be taken into account by the tour leader when they set the duration of the stop in the first place. On this basis there are three scenarios:

• All the clients (and the tour leader) are able to keep to the original time set.

• One (or more) of the clients or the tour leader are unable to keep to the original time set.

• One (or more) clients and one (or more) tour leaders are unable to keep to the original time set.

The following sections derive the estimated deviation from the stated time for each of these scenarios. This deviation has been named the Longdin-Ward Effect in honour of Roger Longdin (a long standing Light & Land client with a track record for working in his own time zone) and David Ward (Light & Land tour leader known for going with the flow while conditions are favourable). These two individuals exemplify the characteristics of the client and tour leader on which these calculations are based.

Disclaimer: It should be noted that the Andrews method for calculating the Longdin-Ward Effect has been based entirely on theoretical examples and anecdotal evidence. To validate the system, it is recommended that extensive trials are undertaken with a variety of client/leader combinations to provide a statistically significant sample.

Definitions: The time estimation process is based on the three point analysis method that is widely used in the commercial world for estimating purposes. Let D_a represent the least time that could be spent. Let D_b represent the most likely time that could be spent. Let D_c represent the most time that could be spent. Then the estimated time (D) is given by:

Now, let D₀ represent the time set by the tour leader at a specific location. The difference between the time set by the leader and the expected duration of the stop is the Longdin-Ward Effect (λω), given by:

Scenario A - All the clients (and the tour leader) are able to keep to the original time set

The best case in this scenario is that everyone will be ready a few minutes prior to the time set by the tour leader. So:

The most likely scenario is that everyone will be ready within a few minutes of the set time. So:

Even with strict time keeping, there is still the chance that something may happen during the stop that will increase the time taken. It is assumed that this will be no more than 25% of the original time. So:

Conversely, to achieve a given time at a location (D_t), the advertised time (D₀) can be expressed as:

Scenario B - One (or more) of the clients or the tour leader are unable to keep to the original time set

The most likely scenario is that everyone will be ready within 5 of the set time, regardless of how long the stop was originally. So:

The worst case is assessed as being an overrun of 50% of the original time set. So:

Conversely, to achieve a given time at a location (D_t), the advertised time (D₀) can be expressed as:

Scenario C - One (or more) clients and one (or more) tour leaders are unable to keep to the original time set

The most likely scenario is that everyone will be ready within 15 of the set time, regardless of how long the stop was originally. So:

The worst case that has been reported is a 1.5 hour dawn shoot at Mono Lake that became a 4.5 hour marathon (largely down to fantastic light rather than poor time keeping, to be fair). So:

Conversely, to achieve a given time at a location (D_t), the advertised time (D₀) can be expressed as:

Corollary: The minimum time for any stop where the full (third order) Longdin-Ward Effect is present is 10 minutes.

The table below sets out the estimated times for each stop for each of the scenarios identified above. The table also calculates the Longdin-Ward Effect associated with each scenario and presents this as a percentage of the original time.

D₀	D₁	D₂	D₃	λω₁	λω₂	λω₃	λω₁%	λω₂%	λω₃%
10	12	14	23	1.92	4.17	13.33	19%	42%	133%
15	17	20	30	2.13	4.58	15.00	14%	31%	100%
20	22	25	37	2.33	5.00	16.67	12%	25%	83%
25	28	30	43	2.54	5.42	18.33	10%	22%	73%
30	33	36	50	2.75	5.83	20.00	9%	19%	67%
35	38	41	57	2.96	6.25	21.67	8%	18%	62%
40	43	47	63	3.17	6.67	23.33	8%	17%	58%
45	48	52	70	3.38	7.08	25.00	8%	16%	56%
50	54	58	77	3.58	7.50	26.67	7%	15%	53%
55	59	63	83	3.79	7.92	28.33	7%	14%	52%
60	64	68	90	4.00	8.33	30.00	7%	14%	50%
65	69	74	97	4.21	8.75	31.67	6%	13%	49%
70	74	79	103	4.42	9.17	33.33	6%	13%	48%
75	80	85	110	4.63	9.58	35.00	6%	13%	47%
80	85	90	117	4.83	10.00	36.67	6%	13%	46%
85	90	95	123	5.04	10.42	38.33	6%	12%	45%
90	95	101	130	5.25	10.83	40.00	6%	12%	44%
95	100	106	137	5.46	11.25	41.67	6%	12%	44%
100	106	112	143	5.67	11.67	43.33	6%	12%	43%
105	111	117	150	5.88	12.08	45.00	6%	12%	43%
110	116	123	157	6.08	12.50	46.67	6%	11%	42%
115	121	128	163	6.29	12.92	48.33	5%	11%	42%

For stops in excess of 2 hours, a basic rule of thumb is to allow for 5% contingency in Scenario A and 10% in Scenario B. Scenario C is likely to perform better in longer stops, as the worst case is not going to be as bad (e.g. it is very unlikely that a 4 hour stop will become a 12 hour stop). It is therefore recommended that extended stops in Scenario C are treated the same as Scenario B, i.e. with a 10% contingency. The table below provides the conversion tables to allow tour leaders to set a duration that is likely to be met.

D_t	D₁	D₂	D₃
10	8	6	0
15	13	11	4
20	18	15	8
25	23	20	11
30	27	25	15
35	32	29	19
40	37	34	23
45	42	38	26
50	47	43	30
55	51	48	34
60	56	52	38
65	61	57	41
70	66	62	45
75	71	66	49
80	75	71	53
85	80	75	56
90	85	80	60
95	90	85	64
100	95	89	68
105	99	94	71
110	104	98	75
115	109	103	79

For example, if you can only stop for 45 minutes, the advertised time should be 42 minutes (Scenario A), 38 minutes (Scenario B) or 26 minutes (Scenario C). If the time is advertised as 45 minutes and you are in Scenario C, you should not expect to leave in under 1 hour 10 minutes.

A L I G H T T H A T N E V E R G O E S O U T

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The Andrews Method for Determining the Longdin-Ward Effect

D_t	D₁	D₂	D₃
10	8	6	0
15	13	11	4
20	18	15	8
25	23	20	11
30	27	25	15
35	32	29	19
40	37	34	23
45	42	38	26
50	47	43	30
55	51	48	34
60	56	52	38
65	61	57	41
70	66	62	45
75	71	66	49
80	75	71	53
85	80	75	56
90	85	80	60
95	90	85	64
100	95	89	68
105	99	94	71
110	104	98	75
115	109	103	79

D_t	D₁	D₂	D₃
10	8	6	0
15	13	11	4
20	18	15	8
25	23	20	11
30	27	25	15
35	32	29	19
40	37	34	23
45	42	38	26
50	47	43	30
55	51	48	34
60	56	52	38
65	61	57	41
70	66	62	45
75	71	66	49
80	75	71	53
85	80	75	56
90	85	80	60
95	90	85	64
100	95	89	68
105	99	94	71
110	104	98	75
115	109	103	79

D_t	D₁	D₂	D₃
10	8	6	0
15	13	11	4
20	18	15	8
25	23	20	11
30	27	25	15
35	32	29	19
40	37	34	23
45	42	38	26
50	47	43	30
55	51	48	34
60	56	52	38
65	61	57	41
70	66	62	45
75	71	66	49
80	75	71	53
85	80	75	56
90	85	80	60
95	90	85	64
100	95	89	68
105	99	94	71
110	104	98	75
115	109	103	79