MOA Math

MOA calculations

In the following, several calculations are introduced, which have the goal of establishing the minimum dimension to be used on an information object. This is done in order to adapt discriminability enhanced information (created using SGD Design principles) to

  1. the requirements of expected viewers and
  2. the conditions of specific scenarios, in which the information is viewed.

The result of the calculation is the dimension to which the Smallest Graphical Detail (SGD) has to be precisely scaled for use on an information object to secure discriminability. With MOA Math, the full potential of the MOA Design Method is taken advantage of, providing the ability to calculate

  • actual size of an information object,
    taking into account viewer’s visus and viewing distance, etc.
  • required viewing distance,
    using viewer’s visus, speed of movement, time etc.
  • maximum supported visus of viewers,
    in case SGD can’t be scaled to calculated MOAd because of space restrictions, or it is impossible to maintain an adequate viewing time, etc.
  • the discriminability of information that was not produced following SGD Design principles
MOA Math calculation operations in relation to scenario and inflexibility of the viewer of information

The complexity of MOA Math calculations to establish or assess discriminability depends on the scenario in which information is used, and the flexibility of the viewer to specific conditions in such a scenario. Inflexibility is the degree to which a viewer is unable to adapt to the conditions for improving the ability to take up the presented information sufficiently. The more specific a scenario becomes, the higher the inflexibility and the need to compensate for it using additional MOA Math calculations.

Basic calculation

  • General scenarios, low viewer inflexibility

For general scenarios, the basic calculation relies on chosen visus and required viewing distance. The resulting (d)imension (SGDd) is applied on information objects in settings with “normal” conditions to provide reliable and inclusive information access. In such general scenarios, it is expected that information is shown (as good as) perpendicular, that there are adequate lighting conditions, etc. Viewers are deemed to have adequate space and time available and may adjust their position in relation to the information to improve it’s uptake.

SGDr is the (r)eference SGD dimension, the size of SGD under the chosen visus at 1 metre viewing distance. To produce SGDd, SGDr is multiplied with the required viewing distance (D) in metre.

SGDr is the (r)eference SGD dimension, the size of SGD under the chosen visus at 1 metre viewing distance. To produce SGDd, SGDr is multiplied with the required viewing distance (D) in metre.

Choosing visus

For this, the question needed to be answered is: “Who is going to use the information?”, and therefore “Who needs to be able to discriminate its components?”. For example, there is information usage, which is restricted to a share of population whose representatives need to have specified abilities concerning eyesight.

According to Council Directive 91/439/EEC of 29 July 1991 on driving licences (Annex III, 6.) – motorists are allowed to bear the following visual acuity:

”Group 1 (drivers of vehicles of categories A, B and B+E and subcategory A1 and B1): (6.1.) Applicants for a driving licence or for the renewal of such a licence shall have a binocular visual acuity, with corrective lenses if necessary, of at least 0,5 when using both eyes together.
Group 2 (drivers of vehicles of categories C, C+E, D, D+E and of subcategory C1, C1+E, D1 and D1+E): (6.3.) Applicants for a driving licence or for the renewal of such a licence must have a visual acuity, with corrective lenses if necessary, of at least 0,8 in the better eye and at least 0,5 in the worse eye.”

Accordingly, the visus chosen to govern SGDr does not need to be lower than 0,5 in such a scenario, which has a decisive effect on the size of SGDd, and total dimension of an information object. The greater the share of the population to use the information needs to be (=the more inclusive) the larger SGDd and the information objects.

Due to its properties, SGD Design accounts for the requirements of several visual impairments. Yet, there are scenarios in which SGDd cannot be applied as planned, but only at a smaller size. In this case, the calculation may be “reversed” to reveal the maximum visus supported, or the actual viewing distance.

Viewing distance

The next question is: “What is the optimal viewing distance?” or “Due to space restrictions of the environment, what is the maximum viewing distance?”.

Viewing distance is the length of the visual field between the eye of the viewer and the information object, which should of course be an unobstructed line of sight. Ideally, a visus is chosen before in order to calculate the optimal viewing distance, which is the one to be applied to information objects for best efficiency. This way, information is as inclusive as planned.

If situations occur where viewing distance is shorter than required, it is a maximum viewing distance. In this case, the actual distance provided in the environment can be measured to adjust SGDd.

For both situations, the above formula can be adapted.

Viewing distance is, in some cases related to required viewing time. This is explained below.

Angle calculation

  • Specific scenarios, medium viewer inflexibility

In some specific scenarios, information might be presented at an angle, and not perpendicular, while the setting would not allow the viewer to adjust position (e.g. to approach a sign). In this case, the angle calculation applies on top of the basic calculation, increasing SGD dimension accordingly.

Angles

Any angular deviation from frontal (perpendicular) view can be measured in degree.

Naturally, seeing for instance a sign at an angle, at some point, reduces the dimensions of white space and graphical elements designed via SGD, below 1 SGDd. As a result, requirements for discriminability are not fulfilled. For instance, if an information object deviates by 60 degrees, SGDd dimension is halved. To compensate, SGDd needs to be doubled. Of course, the angle calculation has its boundries. Very quickly, along with more extreme viewing angles, SGDd dimension increase forces the graphical composition to exceed applicable size as an information object.

The following equations allow to precisely calculate

  1. to which dimension SGDd is reduced as caused by viewing from an angle, and
  2. the required increase in dimension to result in an appropriate SGDd when viewed.
To calculate the reduced size of SGDd (=SGD red) caused by angular view, multiply cosinus α with SGDd. Replace α (=alpha) with the angle (in °) of deviation from perpendicular view.

To calculate the reduced size of SGDd (=SGD red) caused by angular view, multiply cosinus α with SGDd. Replace α (=alpha) with the angle (in °) of deviation from perpendicular view.

To correct the size to SGDd when viewed from an angle, SGDd is divided by SGDred, then multiplied with SGDd, resulting in SGDa (= SGD (a)ngle), which is of increased dimension.

To correct the size to SGDd when viewed from an angle, SGDd is divided by SGDred, then multiplied with SGDd, resulting in SGDa (= SGD (a)ngle), which is of increased dimension.

The table below exemplifies several results from above calculations, but expressed in percentages.

Angle °
% SGDd reduction
Required increase in %
10 98,48 101,543
20 93,97 106,417
30 86,60 115,467
40 76,60 130,539
45 70,71 141,423
50 64,28 155,569
60 50,00 200,000
70 34,20 292,397
80 17,36 576,037

Time/speed calculation

  • Specific scenarios, high viewer inflexibility

In situations where the observation of information is inhibited by time constraints, possibilities for a viewer to adapt and compensate to this are minimal. Inside a moving vehicle (probably steered by the viewer her/himself), there usually is little opportunity to slow down or turn one’s gaze away from the road. In an emergency scenario, where one’s life might rely on fast movement, it’s quite comparable. Both settings might pose severe vision-inhibiting environmental conditions such as glare, smoke etc., and both induce a heightened stress-level, reducing the processing capacity of the viewer.

As in the basic calculation explained, it is the goal to multiply viewing distance (D) with SGDr to produce SGDd. Specifically when moving towards mainly perpendicular oriented information objects at speeds that would reduce viewing time to less than the minimum, viewing distance can be checked and adjusted to extend viewing time. The following calculations to achieve this are from the “Danish technical handbook for VMS”.

CalcSpeedD

D = Viewing (d)istance, a = Distance the information passes out of view (in metre) ,V = (v)elocity, speed in metre per second ,t = viewing (“reading”) time in seconds.

While V x t sets the viewing distance in general, “a” relates to the “point of disappearance”, where parts of an information object pass out of sight, caused by a deviation from the normal (straight-onward) line of sight. A driver, for instance has a field of vision of 15° in vertical due to the limits of a car’s windshield. If “a” applies for a scenario, it equals a specific distance to be added to the viewing distance resulting from v  x  t, to provide adequate viewing time.

CalcSpeedA

Distance “a” is calculated using the field of vision and the offset of an information object from the line of vision. GK = offset of an information object from the line of vision (in metre), α = measured from the line of vision to the edge of the visual field (in degree)

The Danish technical handbook for VMS regulates the amount of time needed to take up information as follows: any information object is attributed with 2 seconds. In addition, per “standard information” in the graphical composition, one-third of a second is granted. As the handbook relates to Variable Message Signs (VMS), it is very likely that one “standard information” refers to a component on the complexity level of a pictogram, symbol, word or phrase, which represent a meaning in itself (=Referent). Lower complexity components such as figures (parts of symbols or typographic characters) which together form a referent may not be taken into account, as the calculation would produce extreme viewing distances and with that, exceeding MOAd dimension.

CalcSpeedT

t = viewing time (in seconds), n= number of “standard information”.

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