Peek-Frank · Source catalogue

A 325-page engineering treatise by F. W. Peek Jr. of General Electric, summarising his 1910-1916 laboratory and field work on high-voltage insulation. Its stated frame is that power transmission needs a dielectric (electric) field as well as a magnetic field, and that insulation fails when the dielectric stress (gradient, volts per cm) exceeds an 'elastic limit' [read: p.22-28 digest]. The best-known contribution is the law of visual corona: the surface gradient at which a wire starts to glow rises as the wire gets thinner, g_v = g_o(1 + 0.301/sqrt(r)) with g_o about 30 kV/cm peak, generalised for air density as g_v = g_o*delta*(1 + 0.301/sqrt(delta*r)). Peek reads this as 'air has a constant strength g_o, but a finite amount of energy of some form is needed to rupture it, so the gradient must hold at g_o over a finite distance 0.301*sqrt(r) cm from the wire' [read: p.65-68, 232-235]. The constants come from a two-group averaging fit ('Sigma-Delta reduction') to polished-wire and cylinder tests; the deep read found that 10 of 19 points were kept, the others discarded as 'probably in experimental error' without a stated criterion, that the algebra of the 'constant strength at a distance' reading is true of any g_v(r) curve, and that no calculation derives 0.301 or the square-root form from ion physics. Peek himself says the form of the rupturing energy 'has not been considered as it was unnecessary' for a working equation [read: p.234]. Companion fits give 31(1+0.308/sqrt r) for wires in cylinders, 27.2(1+0.54/sqrt R) for spheres, and approximate water and oil film constants. Chapter V (digest) describes the outdoor experimental Lines A and B (3/0 cable, 310 cm spacing, 109,500 cm conductor length) and the empirical corona-loss law p = a(f+25)(e-e_o)^2 fitted by the same group-averaging method, with c^2 found proportional to sqrt(r/s). Chapters VIII-IX give the working formulas in metric and English units (e_o = 21.1 m_o r delta ln(s/r) kV; p = (244/delta)(f+25)sqrt(r/s)(e-e_o)^2 x 10^-5 kW/km), irregularity factors, weather and altitude rules, a worked 100-mile three-phase example (e_o = 52.0 kV, which the deep read recomputed and confirmed to 0.2%), comparisons with measured losses on the Leadville (Faccioli), Pittsfield (Hendricks 1906) and Au Sable lines, and a corona-limit-of-voltage table. The deep read found minor misprints (A = 241 vs 244; a cell of Table LXXIX; 'critical voltage may also be decreased by grouping conductors', probably meant 'increased'). Other parts of the book cover sphere-gap and needle-gap spark-over tables (with the average sphere gradient 27.23(1+0.54/sqrt(delta R))), air-density and altitude corrections for insulators, oil and solid insulation (oil strength g_o = 36(1+1.2/sqrt r) kV/cm), fourteen design cases (graded cables, generator-coil corona, bushings, occluded air bubbles stressed 3x), and a data appendix. The appendix reports d.c. vs a.c. tests (d.c. breakdown about equals a.c. peak in air and oil; in varnished cambric d.c. is 1.27-2.59 times the a.c. peak, rising with thickness and time), a Paschen-law table (minimum about 350 V at p*x = 0.05 cm Hg cm), strength of thin air films (161-196 kV/cm at 0.0025 cm, about 35 kV/cm at 0.45 cm), and Peek's 1915 impulse tests with single half-sine waves from 55 to 900 kc: needle-gap impulse ratio from 1.00 up to 2.34, sphere gaps within about 5 percent (hence usable as impulse voltmeters), oil and solid ratios of 2-3.3, rain lowering 60-cycle insulator flashover 36-40 percent but impulse flashover only 2-3 percent, and impulse ratios up to 5.8 at air density 0.05. Peek attributes the impulse results to a 'dielectric spark lag': rupture needs a minimum energy and hence a minimum time [read: p.199]. The scan is a Google digitisation (library stamp dated Feb 18 1971) and the text layer is OCR on 324 of 325 pages; equations and tables are often garbled, so the deep readers worked from page images for the load-bearing formulas. The text states that all experiments are by Peek and GE helpers (H. K. Humphrey thanked in the 1915 preface), except named outside data: Watson (d.c. corona), Whitehead (Table IV compilation, 1917), G. R. Dean (sphere-field formulas), Dubsky (air films, 1914), Bennett (corona current oscillograms), Scott and Mershon (1898 Colorado), Faccioli, Hendricks. [Update after QE] Seven further deep reads were added (see how_read), so every chapter that carries a central claim has now been read from page images, not only digested. (1) Chapter V fitting chain [read: p.159-173, page images]: the quadratic law p = c^2(e-e_o)^2 is stated 'after trial' with no derivation; the Sigma-Delta (two-group) reduction of Line A test 36 used only the 6 highest of 14 points (the low points follow a different law and feed eq. 37). c^2 is printed x10^5 per km (scale confirmed from page image). The frequency offset (f+25) comes from the indoor Table LI (three conductors, one spacing 61 cm, 30-120 cycles); the deep reader's own fits of the outdoor Tables XLVIII-XLIX do not determine the -25. c^2 = 20,500 sqrt(r/s) x10^-5 comes from a 6+6 two-group fit of 12 of 21 outdoor tests (exponent -0.51 rounded to -0.50; nine tests dropped without a stated reason; RMS scatter 8.8% on the 12, 10.1% on all 21). A = 241 is 20,500/85 (60-cycle constant divided by f+25), so it joins two separate fits. The density correction c^2 proportional to 1/delta is called 'not satisfactory' by Peek himself [read: p.171]. The small-conductor law as printed has an extra term: c^2 = 20,500 sqrt((r + 6/s + 0.04)/s) x10^-5 per km (33a), valid for r >= 0.025 cm and s >= 15 cm [read: page image p.173], not (r+0.04)/s as in the digest. Eq. 37, p = q exp(-h(e_o-e)^2), has q (number of spots) and h (size of spots) defined, with listed values (q about 2.5-3.2e-6 per cm, h 0.021-0.030 for tests 30, 105, 103). The temperature series (Table LXII, Line A, 11 tests, -13 to +22 C) gives a line for 1/e_o that Peek draws to -273 C; the deep reader's fitted intercept is -241 to -283 C depending on points kept, and reducing all values to 25 C leaves a 1.4% spread. Humidity (Table LXIII, 10 tests): g_o constant to about 1.3%, but humidity and temperature are confounded. Wind, smoke, fog, snow, sleet: single occasions on Line A, figures only, no wind speeds, none used in a fit. Single-phase: the front matter states 'Tests were made on single-phase lines unless otherwise noted' [read: p.20] and the outdoor appendix says 'These tests were made on comparatively long single-phase lines out of doors' [read: p.286]; Line A has four conductors connected (1 and 3)(2 and 4), so the polarity along the plane is + - + - while Peek uses one spacing s = 310 cm. (2) The only out-of-sample test of the loss law in the book: Fig. 140, corona loss on two parallel wires (s = 67 cm, r = 0.127 cm, 200 cm long) at 100,000 cycles from an Alexanderson alternator, power by unity-power-factor tuning and hot-wire meters. Peek: 'This good check seems to show that the formula applies over a large range, but complete conclusions cannot be drawn from this small amount of data.' About five points. The deep reader finds the slope of the drawn curve matches (34a) with f+25 = 100,025 (about 29.8 W per kV^2 predicted), but the curve's onset (about 16 kV between lines) does not match e_d from (35a)/(36) (about 40 kV between lines), so mainly the frequency scaling is tested. Alexanderson was a GE engineer [memory, high]. (3) Energy-limited breakdown [read: p.199-202]: Hayden and Steinmetz (A.I.E.E. Trans., June 1910): gaps set to 30 kV at 60 cycles (air 0.95 cm, oil 0.16 cm); with a 100 kV transient the oil gap 'will not spark over if the energy applied to the circuit is less than 1.04 joules (4 amp.). For air the minimum energy is 0.45 joule (1.5 amp.)'. Peek adds 'The disruptive energy of oil seems to be about 30 times greater than it is for air' (p.148). The deep reader traced the 4 A (oil) and the 0.95 cm settings to the plotted curves; 1.5 A (air) is an interpolation (about 1.37 A on a straight line); the conversion from amperes to joules is not given and does not follow (1/2)Li^2 for one L (implied 0.13 H vs 0.40 H); the joules are circuit energy, not energy in the gap; the figures plot current, not energy, and show smooth drawn curves with no data points; they support 'spark distance independent of voltage' at low currents (0.25-0.5 A) but not for 2-4 A within the plotted range to about 105 kV; no time is measured. The same pages (Table LXIX, a different experiment by Peek) give 60-cycle versus impulse ratios 2.06-3.58 for oil and 1.35-1.83 for air, so an air gap can protect an oil gap but not the reverse. Stake: Steinmetz and Hayden were GE staff [memory, medium]; the paper itself was not read. (4) Chapter IV [read: p.115-153]: parallel-wire spark-over gradient is linear in spacing with intercept near 30 kV/cm (Table XIX fit 29.4); critical S/r averages 30.1 over nine wires (range 28.4-31.7); the sphere-gap law 27.23 delta(1+0.54/sqrt(delta R)) fits the cask data within 1.5% in 18 of 24 points (worst -3.8%). Peek's accuracy figures are three different things: a 2-3% commercial requirement, a 0.5% repeatability of readings (not a stated accuracy for grounded gaps), and 2% error for calculated curves. Impulse ratios: needle gap 1.20-1.94 (Tables XXXV, XXXVII), 6.25-cm sphere 1.04-1.10 (Table XXXVI) but the impulse voltage is itself read on a 25-cm sphere gap, so a sphere is calibrated against a sphere; calculated impulse voltages from circuit constants agree with sphere readings within 1-2 kV (Table XXXVII). Printing errors found by recomputation: Table XXXVIII delta 0.87 should be 0.77; worked example 2 (p.153) answer 65 kV should be about 74 kV. (5) Chapter III continued [read: p.93-114]: stranded cable m_v = 0.82 decided corona, 0.72 local corona (Whitehead, A.I.E.E. 1911; Table XVI); split conductors: 'the critical voltage is from 20 to 30 per cent. greater than that of a single wire containing the same amount of material' (Peek, p.98) and Whitehead 16% for three wires, 20% for four; so 'decreased' on p.246 is a misprint for 'increased'. Corona diameters by visual : glass lens : quartz lens = 1 : 1.6 : 1.9 (Whitehead 1912), so a large part of corona is ultraviolet; the stroboscope shows positive corona bluish-white and extended, negative red and localised, beaded on polished wire; corona-driven vibration: 'a pair of 20 mil steel conductors, 500 ft. long, were strung at about 10-ft. spacing ... vibrated, starting with a hardly perceptible movement, which in a few minutes had an amplitude of several feet at the center of the span' (fundamental period about 1 s; no date, place or voltage; repeated on short laboratory lengths, Figs. 83-84, motion 'rotary'); Peek reads the half-bright rotation as 'the effect of the stroboscope' at the 60 Hz supply frequency, which sits oddly with a 1 s fundamental. Bennett's oscillograms (A.I.E.E. June 1913) show a sharp positive hump at onset. (6) Chapter VII solid insulation [read: p.202-227]: 'It takes energy and therefore time to rupture insulation'; an insulator may survive nine impulses at three times the 60-cycle puncture voltage and fail on the tenth ('It may be that ...'; no experimenter, date or sample count); oiled pressboard 3.2 mm, 100 kV rapid 60-cycle: impulses to break 100 kV infinity, 140 kV 100, 150 kV 16, 155 kV 2, 165 kV 1. Time law g = g_s(1 + a/T^(1/4)) from one measured curve (14 layers of impregnated paper): fits with a = 0.49 (free exponent -0.257), but g_s = 13.0 is 12% below the 14.7 kV/mm implied by his own table, and for pressboard in oil (Fig. 153) the law with a = 0.5 fails by a large factor. Continuous high frequency lowers oil strength (6.7 kV/mm at 90,000 cycles against 17 at 60 cycles) while a single impulse raises it (39 kV/mm). Loss rises 'approximately' as e^2 and frequency, though the deep reader's slopes are 2.4-2.7. The a.c.-heating explanation rests on Rayner 1912 brass-versus-coated-terminal times, sample temperatures of 118-215 C at puncture, and loss against temperature; partial recovery after rest counts against pure heating. (7) Corona-loss data appendix [read: p.277-294, transcribed]: indoor tests 1B-56B, outdoor Line A and Line B tests. Table LV (12 tests) is outdoor only; 10 of its tests are on pp.287-294 (tests 86 and 77 are not). Voltages in the appendix are between lines (halve for e); losses are for the whole line length. Printing errors listed by the transcriber include several digit slips (tests 26B, 32B, 33B, 45B, 79, 102, 138); delta recomputed from the printed barometer disagrees with the printed delta for tests 138, 125, 126, 80, 79, which matters because corrected c^2 = c^2 x delta. The appendix names no operator, date or place; the Chapter V pages date test 36 to 6 Oct 1910 (inferred) and place the lines in a field east of which lay a city and a factory, unnamed.

Key claims

• The apparent breakdown strength (surface gradient at onset of visible corona) of air around a wire rises as the wire radius falls, following g_v = g_o(1 + 0.301/sqrt(r)) kV/cm peak with g_o about 30 kV/cm, independent of conductor spacing [read: p.64-65, Table I].
• Breakdown of air requires the gradient to be at least g_o over a finite 'energy-storage distance' 0.301*sqrt(r) cm from the surface, so that a finite rupturing energy can be supplied; the form of that energy is left unspecified [read: p.66, 232-234].
• For different air densities g_v = g_o*delta*(1 + 0.301/sqrt(delta*r)), where delta = 3.92 b/(273+t); the density law is supported by the Line A temperature series (e_o reduced to 25 C has a 1.4% spread, Table LXII) and Peek asserts it holds for wires down to delta = 0.02 (an assertion in the text; the deep reads found no table for that range in Ch. III) [read: p.67, 76-82, 233, 183-184].
• The visual critical voltage is independent of conductor material (tungsten, copper, aluminium, iron compared) and is not due to a condensed air film at the surface [read: p.71-72].
• Peek asserts that humidity has no effect on the critical voltage (supported by Table LXIII, 10 Line A tests, g_o constant to about 1.3%, though humidity and temperature are confounded in that table), that fog, rain, sleet, snow and smoke lower it and raise loss (single occasions on Line A, figures only), and that wind has no effect at commercial frequencies (stated without data or wind speeds) [read: p.68, 184-189, 241].
• Corona loss on transmission lines follows p = a(f+25)(e-e_o)^2 with a = (A/delta)sqrt(r/s), A = 241 (p.237) or 244 (p.242), in kW per km of conductor, e_o = m_o g_o delta r ln(s/r) with irregularity factor m_o 1.0 (polished) to about 0.83-0.87 (stranded cable); the fit chain is: quadratic law 'after trial' (Sigma-Delta on the top 6 of 14 points of Line A test 36), f+25 from three indoor conductors at 61 cm spacing, c^2 = 20,500 sqrt(r/s) x10^-5 from 12 of 21 outdoor tests, and A = 20,500/85 = 241 [read: p.159-173, 237-242; calc].
• Calculated corona losses agree with measured losses on practical lines (Leadville, Colorado at high altitude; Au Sable 125-mile line: calculated 15 kW/mile vs 15-20 measured, 'preliminary rough measurements') [read: p.247-248].
• Storm loss can be approximated by taking e_o as 0.8 of the fair-weather value, and the economical operating voltage is the fair-weather e_o; corona will rarely be the limit on transmission voltage, an economic limit comes first [read: p.242, 245-246, 249].
• For a worked three-phase 100-mile line (1/0 cable, 120 in spacing, 1000 ft elevation, 100 F) e_o = 52.0 kV to neutral (about 90 kV between lines) and visual corona starts at 62.6 to 71.3 kV to neutral; the deep read recomputed these as correct [read: p.244-246; calc].
• Air breakdown at very small gaps is much higher than 30 kV/cm: 196 kV/cm at a 0.0025 cm free sphere gap, because the energy-storage distance is cut short (sphere gradient constant between X = 0.54*sqrt(R) and 2R); entrapped air films of the same thickness break down at 161 kV/cm [read: p.82-90, Table IX; p.300].
• Spark-over of sphere gaps follows an average gradient 27.23*delta*(1+0.54/sqrt(delta*R)) kV/cm max (cask data fit within 1.5% in 18 of 24 points, worst -3.8%); Peek's stated sphere-gap accuracies are a 2-3% commercial requirement, 0.5% repeatability of readings and 2% for calculated curves; the sphere-gap impulse ratio 1.04-1.10 is measured against a 25-cm sphere gap [read: p.124-138, 145-147; p.302-303].
• Direct-current breakdown voltage in air and oil equals the a.c. peak, i.e. 1.41 times the a.c. effective voltage; in solid insulation the d.c. gain is larger than 41 percent because a.c. heating weakens the solid [read: p.228, p.295-299].
• Impulse (lightning-like) voltages of a few microseconds need much higher voltage than 60 cycles to break needle gaps (ratio 1.20-2.34), oil (2.06-3.58) and solids (2-3.3), because rupture needs both a minimum energy and a finite time ('dielectric spark lag'); the effect grows as air density falls; no time is measured in the energy-limited-breakdown figures [read: p.145-148, 199-202, 302-306].
• Rain lowers 60-cycle insulator flashover by 36-40 percent (Table VIII) but lowers impulse flashover by only 2-3 percent [read: p.307-308]; the wet flashover of bushings at 50 to 90 percent of dry is a separate figure for a different test (p.151) [read: p.151].
• Air films entrapped in solid insulation break down at about the same gradient as free air gaps of the same thickness, which is why occluded air causes local corona and heating [read: p.300; p.228].
• Electrons, produced and accelerated in the field, are the principal agents of impact ionization (Townsend); ionic saturation at 0.301*sqrt(r) cm from a wire is when corona starts [read: p.231-235].
• Spark-over of a limited-energy circuit depends on the current supplied: Hayden and Steinmetz (A.I.E.E. 1910, a GE investigation) found that gaps set to 30 kV at 60 cycles do not spark over at a 100 kV transient unless the circuit supplies at least 1.04 J (4 A) in oil or 0.45 J (1.5 A) in air; Peek adds that the disruptive energy of oil is about 30 times that of air; the joules are circuit energy, the conversion from amperes is not given in the book, and the paper itself was not read [read: p.148, 199-202; deep read].
• The loss formula was checked outside its fitted range once: Alexanderson's (GE) 100,000-cycle measurement on two parallel wires (s = 67 cm, r = 0.127 cm, 200 cm long, about five points) agreed with (34a), which Peek calls a 'good check' but one from which 'complete conclusions cannot be drawn' [read: p.189, Fig. 140].
• Corona can drive mechanical vibration of conductors: a pair of 20-mil steel conductors 500 ft long at about 10 ft spacing vibrated to an amplitude of several feet at mid-span within minutes, one on the fundamental and one on the third harmonic (period about 1 s), and the effect was repeated in the laboratory (Figs. 83-84) [read: p.113-114].
• Grouping conductors of the same potential raises the critical voltage: 20-30 percent for a split triangle against one wire of the same material (Peek), 16 percent for three and 20 percent for four wires (Whitehead 1911); the p.246 statement 'may also be decreased' is therefore a misprint for 'increased' [read: p.97-98, 246].
• The loss below the quadratic near e_o follows a probability curve p = q exp(-h(e_o-e)^2) (eq. 37), with q set by the number of rough spots and h by their size (Fig. 133, listed values q about 2.5-3.2e-6 per cm, h 0.021-0.030); small conductors follow c^2 = 20,500 sqrt((r + 6/s + 0.04)/s) x10^-5 per km (33a), with a separate disruptive gradient g_d (Table LX) [read: p.173-183, page images].
• Corona contains a large ultraviolet component (apparent diameters by visual, glass lens and quartz lens in the ratios 1 : 1.6 : 1.9, Whitehead 1912), and the stroboscope shows positive corona bluish-white and extended while negative corona is red and localised, forming beads on polished wire [read: p.98-112].
• Insulation damage from impulses is cumulative in solids but not in oil: an insulator may survive nine impulses at three times the 60-cycle puncture voltage and fail on the tenth, and 3.2 mm oiled pressboard survives infinite impulses of 100 kV crest but fails after 100, 16, 2 and 1 impulses at 140, 150, 155 and 165 kV; no experimenter, date or sample count is given [read: p.202, 214-215].
• The time to puncture of solid insulation follows g = g_s(1 + a/T^(1/4)) over infinite time to about 0.01 s (one measured curve, 14 layers of impregnated paper, g_s printed 13.0 kV/mm against 14.7 implied by the table); at very short times Peek ascribes the extra strength to limited energy, at long times to heating [read: p.215-216].

Relevance: This is the only document in the project and it is the source of the 'Peek's law' of corona onset and the empirical corona-loss formula still named after him. It matters here because it states the energy-storage distance idea as a physical hypothesis while presenting the constants as fits, and because the book documents its own experimental method (polished wires, dark room, group-averaged constants) in enough detail to be examined. It is also the primary record of Peek's 1915 impulse tests, an early quantitative account of time lag in breakdown. Interested-party note: Peek worked for General Electric, which had a commercial interest in high-voltage transmission equipment; the preface credits GE's Consulting Engineering Department for the experiments. Interested-party note on the added material: the Hayden-Steinmetz (1910) minimum-energy data and the Alexanderson 100 kHz loss check both come from GE staff; no non-GE test of either is in the book.

Mainstream conflict: Broadly none on the practical formulas: Peek's law remains in use as an engineering estimate [memory, medium confidence]. Points where the text departs from or lags later physics: the 'energy-storage distance' and 'condensed gas film' discussions pre-date the modern ionization and streamer treatment of corona onset; mainstream gas-discharge physics treats breakdown time lag as statistical lag plus formative lag, and a limited-energy circuit as unable to sustain a discharge into an arc, which is a different reading from Peek's dielectric 'minimum energy' [memory, high; not web-checked here]; 'the ether' wording (gamma rays 'probably ether waves', p.230) belongs to pre-relativity physics; 'electron has the same mass as the hydrogen ion' (p.230) contradicts the 1/1800 ratio given in the same passage; the p.246 statement that grouping conductors 'decreased' the critical voltage conflicts with Peek's own data on pp.96-98 (grouping raises it by 16-30 percent) and is read as a misprint. The small-gap high-strength result is explained by Peek's energy distance; the Paschen curve explains it as a point near or right of the minimum (p x = 1.9 torr cm at atmospheric pressure and 0.0025 cm), not the left-hand branch [calc]. No claim here requires new physics.