Fog Index

Fog Index is a measure of reading ease.  Rudolph Flesch devised the following formula to calculate the equivalent years of schooling, needed in that topic, for understanding the information:

Fog Index Formula:

Fog Index = 0.4 x (N + L)
Where: N = Number of three-syllable or longer words per 100 words
L = Average number of words per sentence

To Control Fog Index:

  • Use short sentences (long sentences over 20 words make cumbersome reading)
  • Avoid long, multiple syllable words

Pace

Pace is the speed at which material is presented, and should be adjusted to the complexity of the material and the reader’s familiarity with that topic. There is no pat formula for determining the correct Pace — it is purely subjective.

Why you should consider Pace:

  • If the reader becomes bored and starts skipping ahead, the Pace is too slow
  • If the reader has to reread the material to understand it, the Pace is too fast
  • The reader should understand the material as he or she reads

 

  Topic is Familiar to Reader Topic is Unfamiliar
to Reader
Topic is simple Start fast, continue fast to avoid boring the reader Start slowly to bring reader up to speed, and then speed up
Topic is Complex Start fast to avoid boring reader, and then slow down so reader can understand the material Start slowly and maintain a slow Pace

To Control Pace:

  • Speed up Pace with longer sentences, longer paragraphs, and fewer graphics
  • Slow the Pace with shorter sentences, shorter paragraphs, bullet charts, and graphics

Technical Example
The following example is taken from a technical report for an airplane study. The study sought to determine the lightest weight aircraft for several candidate engines, considering engine size and fuel weight required to fly a specific mission.

 

Fog Index of the above paragraph:

Number of words = 36 (ignoring the article “a”)
Number of sentences = 2
Number of polysyllable words = 7 (shown underlined, ignoring “ing” suffixes, )
Average number of words per sentence = 36/2 = 18
Number of polysyllable words per 100 words = 7 x (36/100) = 2.52
Fog Index = 0.4 (2.52 + 18) = 8.2
(roughly equivalent to an 8th grade education in that subject)

 

Original Draft:

“Engine to engine comparisons were then developed using configuration 7. Figure 1-128 shows the takeoff gross weight (TOGW) of each candidate engine/configuration 7 combination for aircraft concept B (see Figure 0176 in Section 1.1) normalized to the TOGW of the JT15D-5 engine combination. Concepts A and B were considered to be identical insofar as the sizing process was concerned. Ranked in order of TOGW, the LARZAC engine required an increase in TOGW of 4% over the JT15D-5 powered configuration. The TFE 731-2 required 5% and the TFE 731-3 required 6%. The scaled GE27/F1 (A1) required a reduction of 14% but, since it is a paper engine, it was not considered as a realistic contender for the best of the existing engines on the basis of TOGW. The same relative ranking of the engines held for concept C, so JT15D-5 powered versions of configuration 7 were used for Aircraft A, B, and C.”

 

Fog Index is slightly high at 13.3, but the Pace is too fast because of the rapid presentation of data, references, and numbers.

First Revised Draft:

“We studied four engines in order to find the best engine for airplane number 7. Figure 1-128 shows the takeoff gross weight (TOGW) of each study engine on airplane design #7. This is named aircraft concept B. We present these data in Figure 0176 of Section 1.1. These data are normalized to the takeoff gross weight of the JT15D-5 engine. We also studied airplane concepts A and B. We believe these combinations are the same as far as the sizing process was concerned. We then ranked the engines in order of the aircraft takeoff gross weights. We found that the LARZAC engine required an increase in takeoff gross weight of 4% over the JT15D-5 powered airplane #7. We found that the TFE 731-2 engine would increase the airplane’s takeoff gross weight 5% over the takeoff gross weight of the JT15D-5 engine powered airplane #7. We found that the TFE 731-3 engine would increase the airplane’s takeoff gross weight 6% over the takeoff gross weight of the JT15D-5 engine powered airplane #7. We found that the GE27/F1 (A1) engine would reduce the airplane’s takeoff gross weight 14% from the takeoff gross weight of the JT15D-5 engine powered airplane #7. However, this engine was just a study engine, not a real engine. Since it would not be available in time to power the airplane, the GE27/F1 (A1) engine was not considered as the best of the existing engines on the basis of takeoff gross weight. The same relative ranking of the engines held for concept C. Therefore, we used the JT15D-5 powered versions for airplane design #7 for our airplane design A. We used the JT15D-5 powered versions of airplane #7 for our airplane design B. We used the JT15D-5 powered versions of airplane #7 for our airplane design C.”

 

Fog Index is low at 6.5 (i.e., a 6th grade education), but the Pace is much too slow and boring. It is so long (296 words) and so slow, in fact, that it actually inhibits understanding because of the repetition.

Final Revised Draft:
“Use of the JT15D-5 engines resulted in the lightest TOGW for the configuration 7 baseline aircraft, as shown in Figure 1-128. This result is valid for all three aircraft concepts with respect to approach speed and flying qualities. The TOGW would be 4% heavier with the LARZAC engines, 5% heavier with the TFE 731-2, and 6% heavier with the TFE 731-3. Scaled GE27/F1 (A1) engines would have reduced TOGW 14% but they were rejected because they are just “study” engines.”

 

Fog index is reduced to 10.4, and comprehension is greatly improved because Pace is correct for the material being presented. Fog Index is improved by 22%, and word count is reduced from 148 to 78 – a 47% reduction.

Now, here’s the value of setting the correct Fog Index and Pace for your reader: The technical evaluator, who is familiar with the engine designations and subject matter (and is reading a severely page limited competitive Department of Defense proposal for a new contract), will prefer the final revised draft version. The evaluator would find the first revised draft incredibly boring and tedious and would skip ahead. Readers who are neither technically knowledgeable nor familiar with the various airplane and engine nomenclature would much prefer the longer revised draft.
This article illustrates the importance of knowing your readers and writing so they will understand your story. The use of Fog Index and Pace can help you do this. By the way: Due to the technical aspects of most DoD proposals, a Fog Index of about 12 is the best you can usually achieve, and I believe this is okay.