An Experimental and Numerical Thermal Flow Analysis in a Solar Air Collector with Different Delta Wing Height Ratios

This study conducts both numerical and empirical assessments of thermal transfer and fluid flow characteristics in a Solar Air Collector(SAC)using a Delta Wing Vortex Generator(DWVG),and the effects of different height ratios(Rh=0.6,0.8,1,1.2 and 1.4)in delta wing vortex generators,which were not considered in the earlier studies,are investigated.Energy and exergy analyses are performed to gain maximum efficiency.The Reynolds number based on the outlet velocity and hydraulic diameter falls between 4400 and 22000,corresponding to the volume flow rate of 5.21–26.07 m^(3)/h.It is observed that the delta wing vortex generators with a higher height ratio yield maximum heat transfer enhancement and overall enhancement ratio.The empirical and numerical findings demonstrate that the exergy and thermal efficiencies decline in a specific range.TheNusselt number,pressure drop,energy,and exergy efficiencies enhance with rising Reynolds number,although the friction coefficient diminishes.The maximum heat transfer enhancement is 57%.According to the evaluation of exergy efficiency,the greatest efficiency of 31.2%is obtained at Rh=1.4 and Reynolds number 22000.

Finite element analysis on the collapse of infill walls with holes and different length-to-height ratios

Wenchuan earthquake damage survey displayed the major structures of buildings suffered only small damages,but it was common that infill walls suffered heavy damages or even collapse. To study the failure forms and collapse mechanism of infill walls in an earthquake,the influence of opening or length-to-height ratio on shake-resisting capability of filling walls was analyzed,and measures to improve the anti-collapse ability of infill walls were put forwaed. The numerical simulations on collapse process in earthquake were carried out by using ABAQUS software. We used 5 single story and single span models. It is revealed that the rigidity and compressive capacity of infill walls are reduced because of the infill walls with holes and the increases of length-to-height ratios. Adding constructional columns and horizontal beams can ensure structural integrity and improve the anti-collapse ability of the wall.

Dynamics and Wheel's Slip Ratio of a Wheel-legged Robot in Wheeled Motion Considering the Change of Height

The existing research on dynamics and slip ratio of wheeled mobile robot （WMR） are derived without considering the effect of height, and the existing models can not be used to analyze the dynamics performance of the robot with variable height while moving such as NOROS- Ⅱ. The existing method of dynamics modeling is improved by adding the constraint equation between perpendicular displacement of body and horizontal displacement of wheel into the constraint conditions. The dynamic model of NOROS- Ⅱ in wheel motion is built by the Lagrange method under nonholonomic constraints. The inverse dynamics is calculated in three different paths based on this model, and the results demonstrate that torques of hip pitching joints are inversely proportional to the height of robot. The relative error of calculated torques is less than 2% compared with that of ADAMS simulation, by which the validity of dynamic model is verified, Moreover, the relative horizontal motion between fore/hind wheels and body is produced when the height is changed, and thus the accurate slip ratio can not be obtained by the traditional equation. The improved slip ratio equations with the parameter of the vertical velocity of body are introduced for fore wheels and hind wheels respectively. Numerical simulations of slip ratios are conducted to reveal the effect of varied height on slip ratios of different wheels. The result shows that the slip ratios of fore/hind wheels become larger/smaller respectively as the height increases, and as the height is reduced, the reverse applies. The proposed research of dynamic model and slip ratio based on the robot height provides the effective method to analyze the dynamics of WMRs with varying height.

The Effects of Dwarfing Genes (Rht-B1b, Rht-D1b, and Rht8) with Different Sensitivity to GA_3 on the Coleoptile Length and Plant Height of Wheat

Understanding the effects of wheat dwarfing genes on the coleoptile length and plant height is crucial for the proper utilization of dwarfing genes in the improvement of wheat yield. Molecular marker analysis combined with pedigree information were used to classify wheat cultivars widely planted in major wheat growing regions in China into different categories based on the dwarfing genes they carried. The effects of the dwarfing genes with different sensitivity to gibberellins （GA3） on the coleoptile length and plant height were analyzed. Screening of 129 cultivars by molecular marker analysis revealed that 58 genotypes of wheat contained the dwarfing gene Rht-B1b, 24 genotypes of wheat contained Rht-D1b gene and 73 genotypes of wheat possessed Rht8 gene. In addition, among these 129 cultivars, 35 genotypes of wheat cultivars contained both Rht-B1b and Rht8 genes and 16 genotypes of wheat cultivars contained both Rht-D1b and Rht8 genes. Wheat cultivars with the dwarfing genes Rht-B1b or Rht-D1b were insensitive to GA3, while the cultivars with the dwarfing gene Rht8 were sensitive to GA3. Most of the wheat genotypes containing combination of Rht8 gene with either Rht-B1b or Rht-D1b gene were insensitive to GA3. The plant height was reduced by 24.6, 30.4, 28.2, and 32.2%, respectively, for the wheat cultivars containing Rht-B1b, Rht-D1b, Rht-B1b ＋ Rht8, and Rht-D1b ＋ Rht8 genes. The plant height was reduced by 14.3% for the wheat cultivar containing GA3-sensitive gene Rht8. The coleoptile length was shortened by 25.4, 31.3, 28.4 and 31.3%, respectively, in the wheat cultivars containing Rht-B1b, Rht-D1b, Rht-B1b ＋Rht8 and Rht-D1b ＋ Rht8 genes, while the coleoptile length was shortened only by 6.2% for the wheat cultivar containing Rht8 gene. We conclude that GA3-insensitive dwarfing genes （Rht-B1b and Rht-D1b） are not suitable for the wheat improvement in dryland because these two genes have effect on reducing both plant height and coleoptile length. In contrast, GA3- sensitive dwarfing gene （Rht8） is a relatively ideal candidate for the wheat improvement since it significantly reduces the plant height of wheat, but has less effect on the coleoptile length.

Nonlinear mixed-effects height to crown base and crown length dynamic models using the branch mortality technique for a Korean larch( Larix olgensis ) plantations in northeast China

Korean larch(Larix olgensis)is one of the main tree species for aff orestation and timber production in northeast China.However,its timber quality and growth ability are largely infl uenced by crown size,structure and shape.The majority of crown models are static models based on tree size and stand characteristics from temporary sample plots,but crown dynamic models has seldom been constructed.Therefore,this study aimed to develop height to crown base(HCB)and crown length(CL)dynamic models using the branch mortality technique for a Korean larch plantation.The nonlinear mixed-eff ects model with random eff ects,variance functions and correlation structures,was used to build HCB and CL dynamic models.The data were obtained from 95 sample trees of 19 plots in Meng JiaGang forest farm in Northeast China.The results showed that HCB progressively increases as tree age,tree height growth(HT growth)and diameter at breast height growth(DBH growth).The CL was increased with tree age in 20 years ago,and subsequently stabilized.HT growth,DBH growth stand basal area(BAS)and crown competition factor(CCF)signifi cantly infl uenced HCB and CL.The HCB was positively correlated with BAS,HT growth and DBH growth,but negatively correlated with CCF.The CL was positively correlated with BAS and CCF,but negatively correlated with DBH growth.Model fi tting and validation confi rmed that the mixed-eff ects model considering the stand and tree level random eff ects was accurate and reliable for predicting the HCB and CL dynamics.However,the models involving adding variance functions and time series correlation structure could not completely remove heterogeneity and autocorrelation,and the fi tting precision of the models was reduced.Therefore,from the point of view of application,we should take care to avoid setting up over-complex models.The HCB and CL dynamic models in our study may also be incorporated into stand growth and yield model systems in China.

Axial length/corneal radius of curvature ratio and refractive development evaluation in 3-to 4-year-old children: the Shanghai Pudong Eye Study

AIM: To measure and analysis axial length(AL)/corneal radius of curvature(CRC) ratio and other refractive parameters, provide a medical reference range for refractive development evaluation and earlier visual impairment screening of 3 to 4 y kindergarten students.METHODS: Between April and June 2017, a total of 4350 participants aged 3-to 4-year-old(8700 eyes) from 10 cluster random sampling kindergartens in Shanghai, Pudong District were involved. According to the measurement and analysis of the unaided visual acuity(VA), AL, CRC, AL/CRC ratio, astigmatism and other refractive parameters, the data distribution and reference range were obtained.RESULTS: Uncorrected VA of examined children was 0.23±0.08(logMAR, mean±SD) [95% confidence interval(CI) range ≤0.36];AL was 22.10±0.79 mm(95%CI 20.55-23.65);CRC was 7.86±0.26 mm(95%CI, 7.35-8.37);AL/CRC ratio was 2.81±0.12(95%CI, 2.57-3.05). The median of astigmatism was-0.5 D, a total of 56.3% had astigmatism <-0.50 D, 85.3%<-1.00 D, 6.7%>-1.50 D;71% were astigmatism with the rule. Eye-specific analyses were conducted. Statistical difference of VA was in right and left eyes. There were no significant differences between two eyes of AL, CRC, AL/CRC ratio and astigmatism(P>0.05).CONCLUSION: VA and AL/CRC ratio reference could be used to assess refractive development in children and screening uncorrected refractive errors or amblyopia. Astigmatism needs to be considered in the diagnosis.

Research on Two-Step Hydro-Bulge Forming of Ellipsoidal Shell with Larger Axis Length Ratio

The two-step hydro-bulge forming technique was proposed to manufacture the ellipsoidal shell with the length ratio of the long axis to the short axis larger than 1.4. A central tube was introduced into the first step of the hydro-bulge forming process to constrain the over growth of the short axis during bulging,and then the central tube was replaced with two polar plates in the second step of the hydro-bulge forming process to manufacture an integral ellipsoidal shell. It is shown that the central tube restricts the growth of the short axis and simultaneously reduces the shrunk tendency of the long axis. The wrinkling occurs due to the latitudinal compressive stress at the equator at the early stage of hydro-bulge forming. However,with the increase of internal pressure,the compressive stress areas gradually decrease and finally the tensile latitudinal stress occupies approximately the whole shell,thus the wrinkles are eliminated. A sound ellipsoidal shell with the axis length ratio of 1.8 is obtained after two-step hydro bulging.

Stress-strain-acoustic responses in failure process of coal rock with different height to diameter ratios under uniaxial compression

Residual coal pillars play an important role in mining the adjacent coal seam safely,managing the gobs and maintaining the stability of abandoned coal mines.The height to diameter ratio(H/D)affects the stability of residual coal pillars.In this study,uniaxial compressive tests of coal specimens with five H/D(2.0,1.5,1.0,0.8 and 0.6)were performed,and the stress,strain and acoustic emission(AE)were monitored.Results show that the uniaxial compressive strength(UCS)and peak strain increase with H/D decreasing.An empirical equation is proposed to calculate the UCS based on the H/D.The AE activities during coal failure process can be separated into four periods.The span of quiet period and rapid decline period shorten with H/D decreasing.The smaller the H/D is,the more complicated the failure characteristics of coal will be.The failure form of coal with H/D of 2.0,1.5,and 1.0 is primarily shear failure,while splitting failure along the axial direction is the mainly mode when H/D is 0.8 or 0.6.The initiation,expansion,aggregation and connection of micro-cracks can be reflected by the real-time spatial evolution of AE event points.

On the Elastic Vibration Model for High Length-Diameter Ratio Rocket with Attitude Control System

An elastic vibration model for high length diameter ratio spinning rocket with attitude control system which can be used for trajectory simulation is established. The basic theory of elastic dynamics and vibration dynamics were both used to set up the elastic vibration model of rocket body. In order to study the problem more conveniently, the rocket's body was simplified to be an even beam with two free ends. The model was validated by simulation results and the test data.

Effects of Different Sowing Times on Plant Height, Leaf Stem Ratio and DW/FW Ratio of Forage Sorghum in Autumn Idle Land

The aim was to explore the linear regression prediction models between sowing time and plant height, leaf stem ratio and DW/FW ratio of forage sorghum in autumn idle land. [Method] The relationships between sowing time and plant height, leaf stem ratio and DW/FW ratio of forage sorghum were simulated and compared by employing field plot experiment and linear regression analysis. [Result] The sowing time had a great impact on plant height, leaf stem ratio and DW/FW ratio of forage sorghum in autumn idle land. With the delay of sowing time, the plant height and DW/FW ratio of forage sorghum decreased, while the leaf stem ratio increased. The regression models between sowing time and plant height, leaf stem ratio and DW/FW ratio of forage sorghum were established： plant height and sowing time, yheight = 234.725- 5.005X; leaf stem ratio and sowing time,ylcaf= 0.096 ＋ 0,019x; DW/FW ratio and sowing time, ydry= 0.305-0.002X. From July 23rd to August 30th, the plant height of forage sorghum was reduced by 5.005 cm, the leaf stem ratio was increased by 0.019 and the DW/FW ratio was reduced by 0.002 in average when hhe sowing time was delayed by one day. [Conclusion] This study provides a theoretical support for the production of forage sorghum in autumn idle land.

Research on the squeeze cast technology of the castings with large ratio of height to thickness

The squeeze cast technology is only applicable, at present, to the castings with a ratio of height to thickness less than 3.5. Researching the squeeze cast technology for castings with a large ratio of height to thickness will broaden the applicable range of the advanced casting technology. This paper describes a study of the temperature distribution during solidification for castings with a ratio of height to thickness of 7 by the methods of experiment and computer simulation. The shrinkage porosity distribution in the castings and the mechanical properties of the castings were also researched. The experimental and simulated results show that increasing squeeze force, or enhancing mold temperature, cannot reduce the shrinkage porosities in the castings. When castings solidify in a sequential manner and the squeeze force effectively acts on the surface of the liquid metal, the shrinkage porosities in the castings are eliminated and mechanical properties are clearly improved.

Effects of dietary forage to concentrate ratio and wildrye length on nutrient intake, digestibility, plasma metabolites, ruminal fermentation and fecal microflora of male Chinese Holstein calves

Twenty-eight male, weaned Chinese Holstein calves（（156.8±33.4） kg） were used to investigate the effects of dietary forage to concentrate ratio（F：C） and forage length on nutrient digestibility, plasma metabolites, ruminal fermentation, and fecal microflora. Animals were randomly allocated to four treatments in a 2×2 factorial arrangement： whole-length forage（WL） with low F：C（50：50）; WL with high F：C（65：35）; short-length forage（SL） with high F：C（65：35）; and SL with low F：C（50：50）. Chinese wildrye was used as the only forage source in this trial. The grass in the SL treatments was chopped using a chaff cutter to achieve small particle size（-50% particles 〉19 mm）. Dry matter intake（DMI） and organic matter（OM） intake was increased by increasing both F：C（P〈0.01） and forage length（FL）（P〈0.05）, while acid detergent fiber（ADF） and neutral detergent fiber（NDF） intakes were only increased by increasing the F：C（P〈0.01）. The digestibility of NDF was increased as the FL increased（P〈0.01）, and it was also affected by interaction between F：C and FL（P〈0.05）. Cholesterol（CHO）（P〈0.01）, leptin（LP）（P〈0.05）, and growth hormone（GH）（P〈0.01） concentrations in plasma were increased as dietary F：C increased. A significant increase in plasma triglyceride（TG）（P〈0.01）, insulin（INS）（P〈0.05）, and GH（P〈0.01） levels was observed with decreasing dietary FL. Ruminal p H values of calves fed with low F：C diets were significantly lower than those in high F：C treatment（P〈0.05）. Increasing the F：C enhanced ruminal acetic acid（P〈0.05） and acetic acid/propionic acid（P〈0.01）. Fecal Lactobacillus content was significantly higher, while Escherichia coli and Salmonella contents were significantly lower in WL and high F：C groups（P〈0.05）. Lower fecal scores（higher diarrhea rate） were observed in calves fed with SL hay compared to WL hay（P〈0.05）. Denatured gradient gel electrophoresis（DGGE） bands and richness index（S） were significantly affected by the interaction between F：C and FL（P〈0.05）, under high F：C, band numbers and richness index from WL group were higher than that from SL group（P〈0.05）, whereas there were no differences between WL andSL groups under low F：C（P〉0.05）. Microflora similarity was 50–73% among the different treatments. It is concluded that the WL with high F：C（65：35） diet is suitable for weaned calves.

Rational cutting height for large cutting height fully mechanized top-coal caving

Large cutting height fully mechanized top-coal caving is a new mining method that improves recovery ratio and single-pass production. It also allows safe and efficient mining. A rational cutting height is one key parameter of this technique. Numerical simulation and a granular-media model experiment were used to analyze the effect of cutting height on the rock pressure of a fully mechanized top-coal caving work face. The recovery ratio was also studied. As the cutting height increases the top-coal thickness is reduced. Changing the ratio of cutting to drawing height intensifies the face pressure and the top-coal shattering. A maximum cutting height exists under a given set of conditions due to issues with surrounding rock-mass control. An increase in cutting height makes the top-coal cave better and the recovery ratio when drawing top-coal is then improved. A method of adjusting the face rock pressure is presented. Changing the cutting to drawing height ratio is the technique used to control face rock pressure. The recovery ratio when cutting coal exceeds that when caving top-coal so the face recovery ratio may be improved by over sizing the cutting height and increasing the top-coal drawing ratio. An optimum ratio of cutting to drawing height exists that maximizes the face recovery ratio. A rational cutting height is determined by comprehensively considering the surrounding rock-mass control and the recovery ratio. At the same time increasing the cutting height can improve single pass mining during fully mechanized top-coal caving.

Evaluation of axial length/total corneal refractive power ratio as a potential marker for ocular diagnosis of Marfan’s syndrome in children

AIM:To investigate whether the axial length(AL)/total corneal refractive power(TCRP)ratio is a sensitive and simple factor that can be used for the early diagnosis of Marfan’s syndrome(MFS)in children.METHODS:The relationship between the AL/TCRP ratio and the diagnosis of MFS for 192 eyes in 97 children were evaluate.The biological characteristics,including age,sex,AL,and TCRP,were collected from medical records.Receiver operating characteristic(ROC)curve analysis was performed to investigate whether the AL/TCRP ratio effectively distinguishes MFS from other subjects.The Youden index was used to re-divide the whole population into two groups according to an AL/TCRP ratio of 0.59.RESULTS:Of 96 subjects(mean age 7.46±3.28 y)evaluated,56(110 eyes)had a definite diagnosis of MFS in childhood based on the revised Ghent criteria,41(82 eyes)with diagnosis of congenital ectopia lentis(EL)were included as a control group.AL was negatively correlated with TCRP,with a linear regression coefficient of-0.36(R2=0.08).A significant correlation was found between age and the AL/TCRP ratio(P=0.023).ROC curve analysis showed that the AL/TCRP ratio distinguished MFS from the other patients at a threshold of 0.59.MFS patients were present in 24/58(41.38%)patients with an AL/TCRP ratio of≤0.59 and in 34/39(87.18%)patients with an AL/TCRP ratio of>0.59.CONCLUSION:An AL/TCRP ratio of>0.59 is significantly associated with the risk of MFS.The AL/TCRP ratio should be measured as a promising marker for the prognosis of children MFS.Changes in the AL/TCRP ratio should be monitored over time.

Dynamic genetic analysis for body weight and main length ratio in turbot Scophthalmus maximus

The objective of this study was to estimate genetic parameters of body width(BW)to body length(BL)ratio(BW/BL)and of body weight traits(BWT)in turbot,and to elucidate the genetic mechanism of the two traits during ontogeny by dynamic genetic analysis.From 3 to 27 months,BW,BL and BWT of each communally stocked fish were measured every 3 months.The BW/BL ratio was measured at different sampling ages.A twotrait animal model was used for genetic evaluation of traits.The results showed that the heritability values of BW/BL ratio ranged from 0.2168 to 0.3148,corresponding to moderate heritability.The BWT heritability values ranged from 0.2702 to 0.3479 corresponding to moderate heritability.The heritability of BW/BL ratio was lower than that of BWT,except at 3 months of age.Genetic correlation between BW/BL ratio and BWT decreased throughout the measurement period.Genetic correlations were higher than the phenotypic correlations.The current results for estimating genetic parameters demonstrate that the BW/BL ratio could be used as a phenotypic marker of fast-growing turbot,and the BW/BL ratio and BWT could be improved simultaneously through selective breeding.

Preparation of Layered Potassium Titanate Whiskers with Large Length-diameter Ratio by KDC Method

Pure K2Ti4O9 whiskers were prepared by KDC（Kneading-Drying-Calcination） method with TiO2 and K2CO3 as raw materials. The influences of TiO2/K2CO3 molar ratio（RT/K）, calcination temperature（TC） and cooling process on phase composition and morphology of the whiskers were investigated by TG-DSC（thermo gravimetric-differential scanning calorimeter）, XRD（X-ray diffraction）, and SEM（scanning electron microscope）. Pure K2Ti4O9 potassium titanate whiskers with large length-diameter ratio（r）（over 250） can be obtained at RT/K = 2.9 and TC = 950 ℃.

New expressions for the surface roughness length and displacement height in the atmospheric boundary layer

An alternative model for the prediction of surface roughness length is developed. In the model a new factor is introduced to compensate for the effects of wake diffusion and interactions between the wake and roughness obstacles. The experiments are carried out by the use of the hot wire anemometry in the simulated atmospheric boundary layer in a wind tunnel. Based on the experimental data, a new expression for the zero-plane displacement height is proposed for the square arrays of roughness elements, which highlights the influence of free-stream speed on the roughness length. It appears that the displacement height increases with the wind speed while the surface roughness length decreases with Reynolds number increasing. It is shown that the calculation results based on the new expressions are in reasonable agreement with the experimental data.

Change of the mode of failure by interface friction and width-to-height ratio of coal specimens

Bumps in coal mines have been recognized as a major hazard for many years. These sudden and violent failures around mine openings have compromised safety, ventilation and access to mine workings.Previous studies showed that the violence of coal specimen failure depends on both the interface friction and width-to-height（W/H） ratio of coal specimen. The mode of failure for a uniaxially loaded coal specimen or a coal pillar is a combination of both shear failure along the interface and compressive failure in the coal. The shear failure along the interface triggered the compressive failure in coal. The compressive failure of a coal specimen or a coal pillar can be controlled by changing its W/H ratio. As the W/H ratio increases, the ultimate strength increases. Hence, with a proper combination of interface friction and the W/H ratio of pillar or coal specimen, the mode of failure will change from sudden violent failure which is brittle failure to non-violent failure which is ductile failure. The main objective of this paper is to determine at what W/H ratio and interface friction the mode of failure changes from violent to non-violent. In this research, coal specimens of W/H ratio ranging from 1 to 10 were uniaxially tested under two interface frictions of 0.1 and 0.25, and the results are presented and discussed.

Longitudinal Relationship between Axial Length and Height in Chinese Children:Guangzhou Twin Eye Study

Purpose:.To understand the growth model of axial length(AL) and height, and to explore the relationship between the two with the passage of time.Methods:.We followed twins in the Guangzhou Twin Eye Study for five years..The AL of both eyes was measured by partial coherence interferometry, and height was measured by a standard scale during each visit..A multivariate multilevel mixed model was adopted for data analysis.Results:.A total of 1217 children were included in the study.Both AL and height increased, but the rate of growth slowed down with age..The mitigation rate of height growth was-0.34 cm / year;.while that of AL growth was-0.01 mm / year.AL was positively related to height,.with a relevant coefficient of R=0.22(Cov [height intercept, AL intercept] =1.56, 95%CI=1.14 to 1.99). The growth rates of AL and height were also positively related, with a relevant coefficient of R =0.18(Cov [height slope, AL slope] =0.03, 95%CI=0.01 to 0.05).However, taller children had slower rates of height increases,with a relevant coefficient of R=-0.12(Cov[height intercept,height slope]=-1.33,95%CI=-2.25 to-0.42); but had faster AL growth,.with a relevant coefficient of R =(Cov [height intercept, AL slope] =0.02, 95%CI=-0.05 to 0.08, R=0.02).AL and its growth rate were positively related to each other,with a relevant coefficient of R=(Cov [AL intercept,.AL slope]=0.04, 95%CI=0.03 to 0.05, R=0.3); while the growth rates of AL and height were negatively related to each other, with a relevant coefficient of R=(Cov [AL intercept, height slope]=--0.03 95%CI=-0.16 to 0.1, R=-0.02).Conclusion:.The increase in children's AL is relevant to their height increases..The faster their height increases,.the faster their AL increases.

The Paradigm of Surgical Ellipse Dimensions: Are the Length-to-Width Ratio of 3 to 4 and a Vertex Angle of 30&ordm;Correct?

Background: It has been postulated that elliptical cutaneous excisions must possess a length-to-width ratio of 3 to 4 and a vertex angle of 30o or less in order to be closed primarily without creating a “dog ear”. These dimensions became axiomatic in cutaneous surgery and have been taught in the apprenticeship model for years. The present article examines the validity of that paradigm. Methods: We collected data from two sources: ellipses described in the literature (57 cases);and elliptical excisions performed at the authors’ outpatient clinic (83 cases). The surgical ellipse lengths, widths, and vertex angles were analyzed, and the data were compared to a mathematical formula used to generate a fusiform ellipse. Results: The length-to-width ratio of 3 - 4 was found to be inconsistent with the recommended vertex angle of 30o. In fact, a length-to-width ratio of 3 - 4 determines a vertex angle of 48o - 63o. A 30o vertex angle is only feasible with long length-to-width ration of about 7.5. Conclusions: The paradigm that surgical ellipses should have a vertex angle of 30o with length-to-width ratio of 3 - 4 is incorrect. Evidence from actual surgical practice and from mathematical formulation shows that either the length-to-width ratio must be larger than 3 - 4 or the vertex angle must be larger than 30 degrees.