How to find the runway bumps that load the landing gear in the take-off roll

A runway bump that loads the landing gear is a short rise or dip in the longitudinal profile (surface height along the runway) that the wheels meet at take-off-roll speed. To find one, search the profile in distance, tie each event to a chainage (distance along the runway) and an encounter speed, and estimate the dynamic wheel load with a stated model. This guide does that on a synthetic profile, drawing on FAA Advisory Circular 150/5380-9 (30 September 2009) (FAA, 2009) and the FAA-sponsored report DOT/FAA/TC-23/09 (January 2023) (FAA, 2023). It is engineering background, not operational guidance; decisions to operate, restrict or close a runway belong to the aerodrome operator.

Key facts

• An FAA-sponsored research report, DOT/FAA/TC-23/09, describes Type 1 shock, Type 2 short-wavelength and Type 3 long-wavelength runway roughness and calls speed of encounter a primary factor.
• A power spectral density averages a bump's location away, so single bumps are found in the space domain, for example with a rolling chord, and then tied to a chainage and an encounter speed.
• A rolling chord is a screening detector, not the Boeing Bump algorithm of FAA AC 150/5380-9.
• In the synthetic two-mass model in this guide, a 6 m by 20 mm bump and a 30 m by 25 mm bump produce peak dynamic wheel loads of 0.209 and 0.165 of the static load in an accelerating roll.
• Against the wheel load left after lift relief, the later 30 m bump costs at most 0.468 of the remaining load and the earlier 6 m bump 0.309, upper bounds in a synthetic model that is not an aircraft.
• This guide is engineering background and never a judgement on whether a runway may be operated.

What counts as a runway bump that loads the landing gear?

What counts depends on the bump's length, height and the speed at which the wheels meet it. TC-23/09 describes Type 1, a shock (a step, raised slab or very short bump or dip); Type 2, short-wavelength roughness, to which each strut reacts independently; and Type 3, long-wavelength roughness, which excites pitch and plunge and couples main and nose gear. It calls speed of encounter a primary factor (Sec 2.1 to 2.3, pp. 2-3) (FAA, 2023).

Why is a bump found in distance and not in the spectrum?

A power spectral density (PSD) averages a bump's location away; NLR-TP-2009-190 notes it does not distinguish many small bumps from a few large ones (NLR, 2009). See running a PSD on a runway profile for the frequency half.

A rolling chord finds both bumps below. It is not the Boeing Bump algorithm, described in the explainer on FAA AC 150/5380-9.

Narrated film · 2:35

Finding the runway bumps that load the gear

Film made in EffectCraft and FilmCraft from the synthetic traces in calc/.

Read the film transcript

Which bump on a runway loads the landing gear, and how hard? Everything here is synthetic, so every number is invented. A profiler measures surface height along survey lines, the centreline and the main-gear wheel paths. FAA advisory circular 150 slash 5380 dash 9 suggests offsets of three point oh five or five point two two metres. FAA report TC twenty-three slash oh nine describes shocks, short-wavelength and long-wavelength roughness. A spectrum averages a bump's location away, so we search the profile in distance. Our profile has a six metre bump at four hundred and fifty metres and a thirty metre bump at nine hundred. Equation one is the chord deviation. d at position x equals z at x, minus the average of z a half chord behind and z a half chord ahead. Here d is in millimetres, z is profile height, x is chainage, and C is the chord length. At four hundred and fifty metres with a six metre chord, thirty point one two minus the average of ten point eight one and nine point five five gives nineteen point nine four millimetres. We flag peaks above six times a robust spread, which is a screening choice and not a sourced limit. The thirty metre chord gives twenty-four point oh eight millimetres at nine hundred metres. Now model the gear as a sprung mass on a strut, above an unsprung mass on a tyre. Equation two is the dynamic wheel load. Delta F equals k t times the road height z r minus the unsprung height z u. Delta F is the force change in newtons, and k t is tyre stiffness, four million newtons per metre. Divide the peak by the static load of one hundred and seventy point seven kilonewtons. Equation three is lift relief. F s of v equals F s zero times one minus v over V L O F, squared. F s zero is static load, v is ground speed, and V L O F is seventy-five metres per second. At sixty metres per second the squared term is point six four, so only point three six of the static load remains. Now accelerate at two metres per second squared and roll through both bumps. The six metre bump is met at forty-two point four metres per second and peaks at point two oh nine of the static load. The thirty metre bump is met at sixty metres per second and peaks at point one six five. Against the load left after lift relief, the later bump costs up to point four six eight, the earlier point three oh nine. The model is linear, with no rotation, nose gear, thrust, braking or pitch coupling. This is engineering background, and decisions about operating a runway belong to the aerodrome operator. Read the full guide for the method, the code, and the manuals behind it.

How do you find the bumps in a runway profile?

1. Start from a clean profile. Survey at the AC's 0.25 m interval (para 2.2) (FAA, 2009), with chords in multiples of 0.5 m so the half-chord is a whole number of samples; see surveying the centreline and wheel paths.
2. Slide chords over the profile. Compute Equation 1 for a short and a long chord.
3. Set a threshold from the trace. Flag peaks above six times a robust spread, 1.4826 times the median absolute deviation (a screening choice, not a sourced limit).
4. List events by chainage. Merge nearby flags.
5. Tie each event to a speed. Use the aircraft's ground speed at that chainage, not the profiler's: from a stated speed profile or a stated acceleration from the start of the roll. Treat each runway direction and take-off start point (full length, intersection) separately.
6. Estimate the load. Run Equation 2.
7. Apply lift relief. Express the peak against the remaining load (Equation 3).
8. Record what the model left out.

The formula, term by term: chord deviation

Equation 1: d(x) = z(x) − [z(x − C/2) + z(x + C/2)] / 2

symbol	what it is in words	unit	where its value comes from	typical range
d	height of the profile point above the chord joining its two ends (rise positive, dip negative)	mm	computed	synthetic: clean maxima 4.03 mm (6 m) and 8.96 mm (30 m); bump peaks 19.94 and 24.08 mm
z	profile height	mm	the survey	synthetic
x	chainage	m	the survey	0 to 3,000
C	chord length	m	your choice	6 and 30 here; AC straightedges 0.5 to 120 m (para 2.2)

Where it comes from. It is geometry. Join the profile points at x − C/2 and x + C/2 with a chord; d is the mid-point height above it (the average of the two end heights). That is Equation 1, derived, not fitted.

Worked (synthetic). At 450 m with C = 6 m: z(x) = 30.12 mm, z(x − 3 m) = 10.81 mm, z(x + 3 m) = 9.55 mm, so d = 30.12 − (10.81 + 9.55) / 2 = 19.94 mm. At 900 m with C = 30 m: d = 23.97 − (−0.00 − 0.22) / 2 = 24.08 mm.

What it means. It places an event in distance; both bumps stand clear. It is not an assessment; the chord has a wavelength response, gain 1 − cos(πC/λ), which is 2 at λ = C and 0 at λ = C/2, C/4 and so on. One chord is blind to some periodic roughness, so run several and treat the result as screening only.

How does a bump become a wheel load?

Model the gear as a sprung mass m_s on a strut (spring k_s, damper c_s) above an unsprung mass m_u on a tyre of stiffness k_t, driven by road height z_r.

The formula, term by term: dynamic wheel load

Equation 2: ΔF = k_t (z_r − z_u), solved from m_s z̈_s = −k_s (z_s − z_u) − c_s (ż_s − ż_u) and m_u z̈_u = k_s (z_s − z_u) + c_s (ż_s − ż_u) + k_t (z_r − z_u). Static load F_s0 = (m_s + m_u) g. Peak ratio = max|ΔF| / F_s0 and DLC = σ(ΔF) / F_s0.

symbol	what it is in words	unit	where its value comes from	typical range
ΔF	dynamic tyre force change from static	N	computed	synthetic: up to 0.288 F_s0
k_t	tyre stiffness	N/m	SYNTHETIC	4.0e6
m_s, m_u	sprung and unsprung mass	kg	SYNTHETIC	17,000 kg; 400 kg
z_r, z_u, z_s	road, unsprung, sprung heights	m	profile; computed	synthetic
g	gravity	m/s²	constant	9.81
F_s0	static load, (m_s + m_u) g	N	computed	170.7 kN
σ	standard deviation over the run	N	computed	-
k_s, c_s	strut stiffness and damping	N/m; N s/m	SYNTHETIC	1.510e+06; 96133
DLC	dynamic load coefficient	none	computed	synthetic: 0.0144 to 0.0341

Where it comes from. Newton's second law for each mass. The parameters are SYNTHETIC, set from f_s = 1.5 Hz and ζ = 0.30, which give k_s = 1.510e+06 N/m and c_s = 96133 N s/m; with the tyre in series the damped mode is 1.29 Hz. They are not an aircraft's. The synthetic wheel-hop mode is overdamped, so there is no wheel-hop resonance. DLC is a vehicle-pavement measure used for illustration; its aviation use is not sourced.

Worked. F_s0 = (17,000 + 400) kg × 9.81 m/s² = 170.7 kN. At constant speed the peak |ΔF| / F_s0 for the 6 m and 30 m bumps is 0.205 and 0.068 at 20 m/s, 0.207 and 0.136 at 40 m/s, 0.247 and 0.167 at 60 m/s, 0.288 and 0.201 at 75 m/s. DLC barely moves when the bumps go in (at 40 m/s, 0.0208 clean, 0.0237 with bumps), so a peak statistic is needed.

What it means. Met in the roll below, the 6 m bump takes 0.141 s to cross and the 30 m bump 0.500 s. It fails where linearity fails: oleo nonlinearity, a tyre leaving the ground.

How does lift relief change the load as speed rises?

Wing lift takes static load off the wheels.

The formula, term by term: lift relief

Equation 3: V_LOF = √(2W / (ρ S C_L)), and F_s(v) = F_s0 · (1 − (v / V_LOF)²)

symbol	what it is in words	unit	where its value comes from	typical range
V_LOF	speed at which lift at the ground-roll C_L would equal weight	m/s	aircraft data; here set directly	synthetic: 75 m/s
W, S, ρ, C_L	weight, wing area, air density, lift coefficient	N, m², kg/m³, none	aircraft data	not stated
v	aircraft ground speed	m/s	stated speed profile	synthetic
F_s0	static load	N	Equation 2	170.7 kN
F_s(v)	static wheel load at speed v	N	Equation 2	synthetic

Where it comes from. Lift L = ½ ρ v² S C_L. Setting L = W at the ground-roll C_L gives V_LOF; at constant C_L, L / W = (v / V_LOF)², and the wheels carry the rest. A real aircraft rotates at VR and lifts off at a higher C_L, so ground-roll lift stays well below weight: this relief is an upper bound, and the ratios against F_s(v) below overstate it.

Worked (V_LOF synthetic). At 40 m/s: (40 / 75)² = 0.284, so F_s(v) = 0.716 × 170.7 kN = 122.1 kN from unrounded values. At 60 m/s: 0.640, so 0.360 and 61.4 kN.

What it means. The same force is a larger share of what remains, up to this bound. A ratio near 1 is outside the model.

What does a worked roll with two bumps show?

Take the PSD guide's profile with a 6 m × 20 mm bump at 450 m and a 30 m × 25 mm bump at 900 m. The 6 m chord gives 19.94 mm at 450 m (clean maximum 4.03 mm), the 30 m chord 24.08 mm at 900 m (8.96 mm). The 30 m chord also flags 450 m (16.19 mm), so confirm events on the shorter chord.

Accelerate at a synthetic 2.0 m/s² to a synthetic V_LOF of 75 m/s, reached at 1,406 m after 37.5 s. With a constant synthetic acceleration a (m/s²) from rest, v = √(2 a s), where s (m) is the distance from the start; real acceleration falls with speed.

Bump	Met at	F_s(v) / F_s0	Peak |ΔF| / F_s0	Peak |ΔF| / F_s(v) (upper bound)
6 m × 20 mm at 450 m	42.4 m/s	0.678	0.209	0.309
30 m × 25 mm at 900 m	60.0 m/s	0.353	0.165	0.468

F_s(v) is taken at the instant of each peak. The 30 m bump's lower peak is not the smaller load effect: against the load left on the wheels it is the larger, because late in the roll the same bump costs more of what remains. At constant speed, ratios against F_s(v) are 0.289 and 0.189 at 40 m/s and 0.686 and 0.465 at 60 m/s. All values are SYNTHETIC.

What do the FAA research tools do, and what does the model leave out?

APRas, commercial software from APR Consultants rather than FAA software, computes centre-of-gravity and cockpit vertical acceleration at 46.3 m/s (90 kt) (FAA, 2023). In the 2023 report, ProFAA's equations of motion did not allow variable speed (App E, pp. E-3/E-4), so it could not simulate a take-off roll (FAA, 2023) (FAA, 2024c). TC-24/14 recommends adding multiple-event evaluation to the AC and ProFAA (FAA, 2024b). TC-23/09 (Table 1, p. 7) reports the Boeing g criteria, under which a peak vertical load factor (Nz) over 0.80 g at the centre of gravity is unacceptable; APRas output is compared against them; this is research, not FAA policy. NLR-TP-2009-190 (Elaborate Survey, pp. 9-10) says keeping peak vertical acceleration at the gear below 0.35 to 0.40 g is generally considered an achievable and acceptable objective, and no standard criteria for simulation results exist yet (NLR, 2009). AC 150/5380-9 does not address cyclic or harmonic events (FAA, 2009).

The model runs one profile line. The main gear follows the wheel paths, offset from the centreline (AC 2.2f: 3.05 m for airplane design group (ADG) II-III, 5.22 m for ADG IV-VI), and the nose gear another: run the detector on each surveyed line. The model is linear, with no rotation, nose-gear unloading, thrust, braking, pitch-plunge coupling or aircraft natural frequencies. Road practice shares checks with IRI vs rut depth vs texture depth and validating a roughness survey.

What should you keep?

• The profile file, interval, filter, line offset and speed profile.
• Chord lengths, thresholds and flagged chainages.
• Model parameters, each marked aircraft data or synthetic, and the lift-relief assumption.
• The script, its output and the editions cited; research reports are not FAA policy.

The procedure, step by step

1. Start from a clean profile

   Survey at the 0.25 m interval used by FAA AC 150/5380-9 (para 2.2) along the line you care about, and choose chords in multiples of 0.5 m so the half-chord is a whole number of 0.25 m samples.

2. Slide chords over the profile

   Compute the chord deviation d(x), the profile's mid-point height above the chord joining the points at x minus and plus half a chord, for a short chord, such as 6 m, and a long chord, such as 30 m.

3. Set a threshold from the trace

   Flag peaks above six times a robust spread of the deviation trace, taken as 1.4826 times the median absolute deviation. This is the guide's screening choice, not a sourced limit, and it replaces a number copied from another runway.

4. List events by chainage

   Merge flags that lie within one chord length of each other, and note which chord gave the sharpest peak; a long chord also flags a short bump.

5. Tie each event to a speed

   Use the aircraft's ground speed at that chainage, not the profiler's logged survey speed: take it from a stated take-off or landing speed profile, or from a stated acceleration from the start of the roll, v = sqrt(2 a s). Evaluate each runway direction and take-off start point separately.

6. Estimate the dynamic wheel load

   Run a stated two-mass model with the profile as input and record the peak of the dynamic tyre force divided by the static load for each event.

7. Apply lift relief

   Express each peak against the static load left on the wheels at that speed, F_s(v) = F_s0 times (1 minus (v / V_LOF) squared), treat the result as an upper bound because real ground-roll lift is lower, and flag any ratio near 1 as outside the model.

8. Record what the model left out

   State the linear model, the absence of rotation, nose-gear unloading, oleo nonlinearity and thrust or braking, and mark every parameter as aircraft data or synthetic.

Frequently asked

Why can't a power spectral density (PSD) find a single runway bump?

A power spectral density spreads a bump's energy over a band of wavelengths and averages its position away. NLR-TP-2009-190 notes it cannot tell many small bumps from a few large ones at a given wavelength. A space-domain detector, such as a rolling chord, keeps the chainage of each event.

Is a rolling chord the same as the Boeing Bump method in FAA AC 150/5380-9?

No. A rolling chord is a simple screening detector that reports the deviation of a point from the line joining two points a chord apart. FAA AC 150/5380-9 describes the Boeing Bump method and its index separately, and this guide does not reproduce it.

Why does the same runway bump matter more later in the take-off roll?

Wing lift carries a growing share of the aircraft as speed rises, so the static wheel load falls. In the synthetic model, the 30 m bump gives a lower peak than the 6 m bump against the full static load but a larger one against the load left, an upper bound because real ground-roll lift is lower.

Does ProFAA simulate the take-off roll?

As described in the 2023 FAA-sponsored report DOT/FAA/TC-23/09, ProFAA could not simulate a take-off roll: the report states in Appendix E (pp. E-3/E-4) that ProFAA's equations of motion did not allow variable speed. APRas, commercial software, computes accelerations at a constant simulated 46.3 m/s (90 kt).

Where this connects

The hub, runway surface thresholds and the documents that set them, says which limits apply. Boeing Bump Index vs IRI vs straightedge compares the measures; from runway survey to rehabilitation decision follows the findings onward.

References

1. FAA (2009). AC 150/5380-9, Guidelines and Procedures for Measuring Airfield Pavement Roughness. 30 Sep 2009, no revision letter, Active. Original source.Foreword; para 1.2b-g; para 2; 2.1; 2.2a-g; 2.3a-b; 2.4a-d; 2.5a-b; Fig 2-3; Fig 2-4; Ch 3 (3.1, 3.2)
2. FAA (2023). Method to Identify and Quantify Multiple-Event Roughness, DOT/FAA/TC-23/09 (T. Gerardi, M. Gerardi, APR Consultants). Final Report, January 2023 (does not constitute FAA policy). Original source.Exec summary pp. ix-x; Sec 2 p. 2; Sec 2.1-2.3 pp. 2-3; Sec 3 p. 4; Sec 3.1 p. 9; Table 1 p. 7; App E pp. E-3/E-4, E-8/E-9
3. FAA (2024b). Airport Pavement Multiple-Event Roughness Detection and Evaluation, DOT/FAA/TC-24/14 (T. Gerardi, M. Gerardi). Final Report, August 2024 (does not constitute FAA policy). Original source.Exec summary; Sec 2.2, 2.3, 3.2, 3.3; 5.1.1-5.1.3; acronym list
4. NLR (2009). Evaluation Methods for longitudinal evenness of runway pavements: An overview of recent Dutch experiences, NLR-TP-2009-190 (P.A. van Gelder, M.J.A. Stet). June 2009. Original source.Sec 1 pp. 5-6; Sec 2.1 p. 7 and Table 1; 2.2; Elaborate Survey pp. 9-10; 3.1 p. 11; 3.3 p. 13; 3.5 p. 16; 4 p. 18
5. FAA (2024c). ProFAA roughness software. ProFAA 3.1.0 (MER function), FAA Airport Technology R&D; release date unconfirmed. Original source.AC 150/5380-9 Ch 3 (2009 behaviour); TC-23/09 App E (2023 limits)

Use the manual edition and project requirements that apply to your work. Worked examples use synthetic values and are not site-specific design advice.