Put a variable frequency drive on a vertical turbine pump and you have done something the pump was never designed for: you have made its running speed adjustable. A constant-speed pump runs at one speed its whole life, and the manufacturer only had to make sure that one speed was safe. A pump on a drive sweeps through every speed between its minimum and 60 Hz, every time it starts.
Somewhere in that sweep there is usually a speed the machine should not sit at.
That is what a skip band is. It is a range of drive frequencies the VFD is programmed to pass through quickly and never dwell in, because the pump has a natural frequency there and running on top of it shakes the machine apart.
Not immediately — that is exactly what makes it expensive. A pump running a few percent away from a natural frequency does not fail today. It wears lineshaft bearings, loosens the discharge head bolting, fatigues the baseplate grout, and arrives at the shop years before it was due. Nobody budgets for that as resonance. It gets written up as a pump pull.
And the pull is the real cost. A district plans its capital around an interval — this well gets pulled every eight or ten years, and that is what the replacement fund is sized for. A machine sitting on a natural frequency does not shorten a long life by a little; it can halve the interval. You pay for a second pull, a second rental, a second outage and a second crew inside the window you had budgeted one. The equipment did not fail early against some theoretical twenty-year life it never had. It failed early against the service interval the district actually planned and funded — and that gap is the entire loss.
This note is about where those numbers come from, because a vertical turbine has four separate frequencies that matter, they come from four different places, and only two of them can be worked out from a well record.
Four frequencies, four sources
1. The lineshaft’s lateral critical. The shaft between the motor and the bowls is a long, thin beam held by bearings every 5 or 10 feet depending on the design. Like any beam it has a frequency at which it wants to bow sideways. This one is geometry: shaft diameter and the distance between bearings.
2. The structure’s natural frequency — the reed. The motor sits on a discharge head, which sits on a foundation, and that whole assembly behaves like a reed: clamped at the base, free at the top, waving. This is the one that cannot be calculated from a well record, and it is also the one most often quoted wrongly, because the number on the motor data sheet is not the frequency of your installation.
3. The rotor’s torsional modes. The motor rotor, the lineshaft and the impellers form a twisting system, not just a bending one. Torsional modes are usually well below running speed on a vertical turbine — the analysis we cite below puts the first at 7.9 Hz, or 474 rpm — which is why most articles skip them. On a fixed-speed pump that is fair. On a drive it is not: 474 rpm is inside the ramp, and every start passes through it.
4. The impellers’ vane pass. Not a natural frequency at all, but a forcing frequency: every time a vane passes the discharge nozzle it delivers a pressure pulse. Six vanes at 1,770 rpm is 177 pulses per second.
The first three are what the machine wants to vibrate at. The fourth is one of the things making it vibrate — along with residual unbalance at 1× running speed and misalignment at 2×.
What goes wrong is resonance: a forcing frequency arriving at a natural one. The structure stops absorbing the energy and starts storing it, and the same small force that produced a thousandth of an inch of motion produces ten or twenty times that. How much worse depends on two things — how close the two frequencies are, and how much damping the structure has. An above-ground vertical turbine is a lightly damped structure. There is very little in a motor stand and a discharge head to turn vibration into heat, which is why the amplification can be large and why the separation margins in this business are as wide as they are.
The lineshaft critical, and why it is a ceiling
The first lateral critical of a lineshaft follows the classic beam relationship: it rises with shaft diameter and falls with the square of the bearing spacing.
N ≈ 4.77 × 10⁶ × d ÷ L²
N is the first lateral critical in rpm, d the shaft diameter in inches, L the bearing spacing in inches.
That constant is not a handbook curiosity. It falls out of the elastic modulus and density of steel — more precisely it is 4.767 × 10⁶ — and you can derive it from first principles in a line of algebra, which means you can also check it.
And it holds up. We compared it against a manufacturer’s finite-element dynamic analysis for a recent three-well replacement: a 1.937 in open lineshaft on 60 in bearing centers, modeled with added water mass, impeller masses, bearing stiffness and motor rotor inertia. The finite-element model returned a first lateral mode at 41.9 Hz — 2,514 rpm. The formula gives 2,565 rpm. Two percent apart, and the formula lands on the high side, which is where a ceiling belongs.
The squared term is the whole story. Doubling the bearing spacing does not halve the critical speed — it quarters it.
Bearing spacing is not a free choice. Vertical turbine specifications set the maximum, and it depends on how the shaft is carried and how fast it turns:
- Open lineshaft, water-lubricated: spacing shall not exceed 10 ft at speeds up to 1,800 rpm, and no greater than 5 ft above 1,800 rpm.
- Enclosed lineshaft, oil-lubricated inside the enclosing tube: 5 ft.
Work both. A 1-11/16 inch (1.6875 in) shaft on five-foot spacing — an enclosed lineshaft, or an open one turning above 1,800 rpm:
N = 4.767 × 10⁶ × 1.6875 ÷ 60² = 2,234 rpm
That machine runs below its first lateral critical. Now the same shaft on the ten-foot spacing an open lineshaft is normally built to, with nothing else changed:
N = 4.767 × 10⁶ × 1.6875 ÷ 120² = 559 rpm
Same shaft, same motor, and the critical is now a third of the running speed. That is normal, and it is not a defect. An open lineshaft turbine at 1,770 rpm is designed to run above its first lateral critical and to accelerate through it on the way up — across the line, the whole speed range is crossed in the seconds it takes the pump to come up, and nothing has time to build.
But notice what just happened to the answer. One assumption about bearing spacing moved the first critical by a factor of four and flipped the machine from sub-critical to super-critical. Those are not two values of one number; they are opposite descriptions of the same pump. Some manufacturers do specify 5 ft on an open lineshaft precisely to keep the machine below its first critical — the analysis above is one of them. So the bearing spacing is not a detail to assume. It is on the pump submittal, it is one number, and until it is on your record the critical speed is a range rather than a value.
What changes all of this is a drive. On a VFD the operator can hold the machine at a speed it was only ever meant to pass through. The critical did not move; the ability to sit on it is what is new.
Treat any number this formula gives you as a ceiling, not a value. It assumes uniform spacing, a straight shaft and rigid bearings, and every departure from that lowers the real critical: a worn bearing, a longer bottom span, a bent section, the added mass of the water the shaft turns in, and the axial down-thrust a deep setting carries, which softens a beam in bending. If the calculation says 559 rpm, the machine’s true first critical is 559 rpm or less.
The reed frequency, which nothing can derive — and which is not the number on the data sheet
Here is the part most articles skip, and the part most of the rest get wrong.
A vertical motor has a published reed critical frequency (RCF). It is a real, manufacturer-supplied number, and you should absolutely get it. But read its definition carefully: the RCF of an electric motor is the first natural frequency of the vertical motor mounted on a rigid and massive base.
Your discharge head is not a rigid and massive base. Neither is your foundation.
The motor’s RCF is a property of the motor alone, established on a test stand deliberately built to contribute no flexibility of its own. The frequency that matters to you is the natural frequency of the installed assembly — motor, discharge head, sole plate, grout and foundation acting together. The head is a spring and the motor is the mass on top of it; adding the head and the foundation adds flexibility in series with the motor’s own, and adding flexibility always lowers a natural frequency. The installed system frequency is essentially always below the motor’s published RCF, and it can be well below it.
The dynamic analysis we cited earlier shows exactly this. The motor’s RCF went into the model as a design input at 54 Hz. The assembled above-ground structure came out at 40.1 Hz and 40.9 Hz — around a quarter lower than the motor alone. A skip band drawn around 54 Hz would have protected a frequency the installed machine does not have, and left the two it does have completely uncovered.
This is also why NEMA MG 1 asks vertical motor manufacturers for more than the RCF. It calls for the motor’s weight, the height of its center of gravity and its static deflection — precisely so that a pump builder can combine the motor with the structure underneath it and compute the system frequency. The RCF on its own was never meant to be the answer; it was meant to be an input.
So the honest position on any given well is:
- RCF on the motor data sheet — go and get it. One number, and nothing else can produce it. There is no relationship between horsepower and reed frequency you can rely on, no lookup table, and no way to infer it from a well record. If it is not on file, the honest answer is that you do not know it — not a plausible number.
- Installed system frequency — this needs the head and foundation too. It comes from the pump builder’s structural analysis, or from a bump test on the actual machine. It is the number a skip band should be drawn around.
And this matters for procurement more than most people realize. When a district replaces a motor, the reed frequency of the new one is rarely part of the conversation. Two 300 hp motors from different manufacturers, on the same pump, have different RCFs and different centers of gravity — which means a different installed system frequency on an unchanged discharge head. A pump that ran smoothly for fifteen years can come back shaking because of a motor swap that looked like a like-for-like replacement on paper.
Where a frequency becomes a speed
A natural frequency is in hertz. A drive setting is in hertz. But they are not the same hertz, and confusing them is the most common mistake in this whole subject.
A structural frequency of, say, 31 Hz is 31 cycles per second of the assembly swaying. The drive’s 31 Hz is an electrical frequency that produces a shaft speed. To find out whether they meet, you have to convert — and the answer depends on which excitation you are asking about. Take a 1,770 rpm motor at 60 Hz. Shaft speed is proportional to drive frequency, so:
- 1× (unbalance) excites at running speed. To make running speed equal 31 Hz — that is, 1,860 rpm — the drive would have to output 63.1 Hz. Above the usable range. Harmless.
- 2× (misalignment) excites at twice running speed, so it reaches 31 Hz when running speed is 15.5 Hz, or 930 rpm — a drive output of 31.5 Hz. That is squarely in the operating range, and it is the coincidence that matters.
- Vane pass with six vanes excites at six times running speed, reaching 31 Hz at 310 rpm — a drive output of 10.5 Hz. Below any sensible minimum speed, so the pump only crosses it on the way up.
Same motor, same frequency, three completely different answers. One is unreachable, one is a real hazard, one is a start-up transient. A skip band drawn around “31 Hz” without doing this conversion would protect the wrong part of the range entirely. The drive-frequency conversion is the same proportion the affinity laws use, and the speed calculator will do it for any motor.
What separation is enough — and why the answer depends on your evidence
There is a temptation to look for the one correct percentage. There isn’t one, and the reason is worth understanding, because it is the single most useful idea in this note.
The margin you need is a function of how good your number is. Published practice sets it in tiers:
| What you have | Typical separation margin |
|---|---|
| A simplified or formula-based estimate (a “Level 1” analysis) | +35% / −25%, and not less than ±25% |
| A detailed finite-element analysis (a “Level 2” analysis) | ±20% |
| A measured frequency from a bump test on the actual machine | ±10% field acceptance |
That is not three opinions. It is one principle. A number you calculated from shaft diameter and an assumed bearing spacing could be twenty percent off, so you stay twenty-five percent away. A number a finite-element model produced with the real masses and stiffnesses is good to a few percent, so twenty percent will do. A number you measured on that machine last Tuesday only has to clear the physics, and ten percent is enough.
It follows that widening the band is not the conservative choice — it is the expensive one. On a VFD, every hertz inside a skip band is a hertz the pump cannot operate at, and the skipped range is often right where the pump would run most efficiently at reduced flow. Buying a better number buys back operating range.
Where this lands in practice: a project specification will usually state its own margin, and that governs. On the three-well analysis quoted above, the specification required frequencies to be ±25% of the operating range, and the manufacturer’s report applied exactly that as its acceptance criterion. Waterwell IQ™ uses ±25% on a frequency it has estimated from geometry, for the reason in the table — our estimate is a Level 1 number, and it is entitled to a Level 1 margin. Where a district holds a real analysis or a measured frequency, that number and its tighter margin should replace ours.
Draw the band around the operating range, not around one speed
This is the mistake that survives even in careful work, and it exists only because of drives.
On a fixed-speed pump there is one running speed, so “keep the natural frequency 25% away from running speed” is a complete instruction. On a VFD there is no such thing as the running speed. There is an envelope — and the natural frequency has to clear the whole envelope, not the speed the pump happens to be at today.
The analysis we have been quoting does it properly. The pump’s stated operating range is 900 to 1,800 rpm. Applying ±25% to the ends of that range, not to a single point, gives an avoidance band of:
675 rpm to 2,250 rpm — every natural frequency must fall outside this.
Check the same machine against its rated 1,770 rpm alone and a natural frequency at 1,000 rpm looks clear by a mile. It is not clear at all. It is the speed the operator reaches the first time they turn the drive down, which is the entire reason the drive is there.
So: take the minimum speed the drive is programmed to allow, take the maximum, apply the margin outward from both ends, and require every natural frequency you know about to sit outside the result. If your VFD minimum is set at 30 Hz, say so in the analysis — lowering it later is a change to the machine’s safety case, not just a setpoint.
The manufacturer’s band always wins
If the pump maker published a skip band or a dynamic analysis on the submittal, program that one. It came from someone who had the drawings, the real masses and often a measured test of that specific assembly. A calculation from a well record cannot beat it, and it should never quietly replace it.
Read the report properly when you get one, because a good analysis says more than pass or fail. A well-written results table lists every mode, whether it falls inside the avoidance range, and how much of the structure’s mass actually participates in it. A mode inside the range with under 5% effective mass participation is routinely accepted and remarked as such — it is a mode nothing can excite hard enough to matter. On the analysis quoted here, three below-ground modes sit inside the avoidance range at 0% participation and are accepted; the two above-ground modes, where the mass is and where people stand, are held to the range strictly. A reviewer who sees “inside range” and stops reading will reject a machine the analysis correctly passed.
Where a calculated band is useful is when there is no published one — which is most of the time on a well that was re-equipped in 1998 by a contractor who is out of business. Then an estimate with its assumptions stated is far better than an empty field, so long as everyone knows which it is.
What to do with this on Monday
- Find out whether the drive has skip frequencies programmed at all. Many do not. It is a parameter, and it is often left at factory default.
- Get the reed frequency onto the record — and know which one you have. The motor data sheet gives you the motor’s RCF on a rigid base. That is an input, not the answer. If the pump builder’s structural analysis exists, the installed system frequency is in it; if it does not, a bump test on the machine will give it to you in an afternoon.
- Record which lineshaft you have, and get the spacing off the submittal. Open or enclosed changes the assumption, and the formula squares the spacing — the difference between 5 ft and 10 ft is a factor of four in the answer and can flip the machine from sub-critical to super-critical.
- Write down the drive’s actual minimum speed, and draw the band around the range between it and 60 Hz, not around the rated speed.
- Check it again after any motor change. The reed frequency belongs to the motor, and the installed frequency belongs to the motor and the head it is bolted to.
- Write the band into the O&M record, not just the drive. The parameter lives in a box on a wall that will be replaced one day by someone who was not there.
Quick answers
What is a skip band on a VFD?
A range of output frequencies the drive is programmed to pass through without stopping, because running there would put a forcing frequency on one of the machine’s natural frequencies. It is set as a parameter in the drive and should also be written into the pump’s O&M record.
Is running a vertical turbine above its first critical speed a problem?
Not by itself. An open lineshaft on 10 ft spacing at 1,770 rpm normally runs well above its first lateral critical and passes through it in seconds on start-up. It becomes a problem when a drive lets the machine dwell near that speed.
Where do I find a pump’s reed frequency?
The motor’s RCF is on the motor data sheet, but it is measured on a rigid base. The frequency that matters, the installed system’s, comes from the pump builder’s structural analysis or a bump test on the machine. See critical speed in the glossary, and how to read a pump curve for how speed moves the duty point.
See the critical speeds and skip bands the record implies for one of your own wells. Request a walkthrough →
Sources
- Hydraulic Institute. ANSI/HI 9.6.8, Rotodynamic Pumps — Guideline for Dynamics of Pumping Machinery. Source for natural-frequency analysis scope and separation-margin practice on vertical pumps.
- NEMA. ANSI/NEMA MG 1, Motors and Generators, vertical motor sections. Source for the motor manufacturer as the origin of a vertical motor’s reed critical frequency, and for the weight, center-of-gravity height and static deflection supplied so a system frequency can be computed.
- National Pump Company. Structural Natural Frequency Analysis. Source for the tiered margins: +35%/−25% and not less than ±25% for a Level 1 analysis, ±20% for a Level 2 analysis, ±10% field acceptance; and for the discharge head acting as the spring under the motor’s mass.
- U.S. Patent 11,594,935. Normalizing lateral reed critical frequency in vertical electric machines. 2023. Source for the definition of RCF as the first natural frequency of the motor mounted on a rigid and massive base, and for the installed system having its own reed frequency.
- Taco. VT Series Vertical Turbine Pump, Water Lubricated — Specifications. Source for the bearing spacing limits: not to exceed 10 ft up to 1,800 rpm, no greater than 5 ft above it.
- WaterWorld. Special Vibration Considerations for Vertical Turbine Pumps. Source for analyzing natural frequencies up to 1.25 × vane pass, and for locking speed ranges out of a VFD.
- Manufacturer’s finite-element dynamic analysis issued with a three-well vertical turbine submittal, reviewed 2026 (not published). Source for the comparison of 41.9 Hz from the model against 42.8 Hz from the formula, the motor RCF of 54 Hz against assembled structural modes at 40.1 and 40.9 Hz, the first torsional mode at 7.9 Hz, the 900–1,800 rpm envelope with its 675–2,250 rpm avoidance band, and the 5% mass-participation exemption.
Every link above was retrieved and read on 2026-09-25. Paid standards are named by designation so you can check them against your own copy.